8.OPTICS

OPTICS

DHANALAKSHMI NAGAR NEAR ANNAMAIAH CIRCLE, TIRUPATI. PH NO. 9440025125

OPTICS

Review of Concepts (a) (B)

Due to reflection, none of frequency, wavelength and speed of light change. Law of reflection : (i) Incident ray, reflected ray and normal on inident point are coplanar. (ii) The angle of incidence is equal to angle of reflection.

Some important points : In case of plane mirror : (i) For real object, image is virtual. (ii) For virtual object, image is real. (iii) Image size = Object size. (iv) The converging point of incident beam behaves as object. (v) If incident beam on optical instrument (mirror, lens etc) is converging in nature, object is virtual. (vi) If incident beam on the optical instrument is diverging in nature, the object is real. (vii) The converging point of reflected or refracted beam from an optical instrument behaves a image. (viii) If reflected beam or refracted beam from an optical instrument is converging in nature, image is real.

n P

P

Real Image

n

Virtual Object

n

(ix) If reflected beam or refracted beam from an optical instrument is diverging in nature, image is virtual.

  P’

P n Real Object

 

Virtual Object

(x) For solving the problem, the reference frame is chosen in which optical instrument (mirror, lens, etc.) is in rest. (xi) The formation of image and size of image is independent of size of mirror.

(xii) Visual region and intensity of image depend on size of mirror.

www.physicsashok.in

1

OPTICS (xiii) If the plane mirror is rotated through an angle  , the reflected ray and image is rotated through an angle 2  in the same sense. (xiv) If mirror is cut into a number of pieces, then the focal length does not change. (xv) The minimum height of mirror required to see the full image of a man of height h is h/2. v sin

Rest

Rest

v sin

Object



v

Image

Object

v cos Image

v cos

(xvi)

(xvii)

Rest vm

vm Object

v

Image

2 vm - v

vm

v

2 vm

(xix)

(xviii)

Object

Image

Object In rest

Image

2 vm + v

(xx) (C) Number of images formed by combination of two plane mirrors : The images formed by combination of two plane mirrors are lying on a circle whose centre is at the meeting points of mirrors. Also, object is lying on that circle. 360  where  = angle between mirrors.

Here, n 

(i) If

360 is even number, the number of image is n–1. 

360 is odd number and object is placed on bisector of angle between mirrors, then  number of images is n–1.

(ii) If

360 is odd and object is not situated on bisector of angle between mirrors, then the  number of images is euqal to n.

(iii) If

(D)

n

Law of reflecteion in vector form : Let eˆ1 = unit vecotr along incident ray..

nˆ

Let eˆ 2 = unit vector along reflected ray

ˆ 1

ˆ 2

nˆ = unit vector along normal on point of incidence Then, eˆ 2  eˆ1  2 eˆ1 . nˆ nˆ

(e)

Spherical mirrors : (i) It is easy to solve the problems in geometrical optics by the help of co-ordinate sign convention.

www.physicsashok.in

2

OPTICS y

y

x x’

x’ y’

y

x x’ y’

(ii) The mirror formula is

y

y

x x’ y’

x x’

x

y’

y’

1 1 1    u 

Also, R = 2  These formulae are only aplicable for paraxial rays. (iii) All distances are measured from optical centre. It means optical centre is taken as origin. (iv) The sign convention are only applicable in given values. (v) The transverse magnification is image size     object size u Sun 1. If object and image both are real,  is negative. 2. If object and image both are virtual,  is negative D F  3. If object is real but image is virtual;  is positive.  4. If object is virtual but image is real,  is positive. d 5. Image of star; moon or distant object is formed at focus of mirror. If y = the ddistance of sun or moon from earth. D = diameter of moon or sun’s disc.  = focal length of the mirror d = diameter of the image  = the angle subtended by sun or moon’s disc D d  Then tan  =  = y  Here,  is in radian.

Laws of Refraction 1.

(a)The incident ray, the refracted ray and normal on incidence point are coplanar.

1 1 (B) 1 sin 1   2 sin 2    cons tan t .

2 2

nˆ ˆ 1

1

(C) Snell’s law in vector form: Let,

eˆ1 = unit vector along incident ray

ˆ 2

2

eˆ 2 = unit vecotr along refracted.

www.physicsashok.in

3

OPTICS nˆ = unit vector along normal on incidence point. Then 1 eˆ1  nˆ   2 eˆ 2  nˆ .

Some important points : (i) The value of absolute retractive index  is always greater or equal to one. (ii) The value of refractive index depends upon material of medium, colour of light and temperature of medium. (iii) When temperature increases, refractive index decreases. (iv) Optical path is defined as product of geometrical path and refractive index. i.e., optical path =  x (v) For a given time, optical path remains constant. i.e.,

1 x1   2 x 2   cons tan t



1



1 c1   2 c 2  2 c1  1 c 2



i.e.,

dx 1 dx 2  2 dt dt



1 c

(vi) The frequency of light does not depend upon medium. c1   1 , c2   2  1 c 2  2 1      2 c1 1  (a) When observer is in rarer medium and object is in denser medium: real depth  Then apparent depth (B) When object is in air and observer is in denser medium: Apparent Real depth P’ apparent position depth  real position

2.

Air Observer

Denser medium () P

Object

t  1 (C) The shift of object due to slab is x  t 1     (i) This formula is ony applicable when observer is in rarer medium. (ii) The object shiftness does not depend upon the position of object. (iii) Object shiftness takes place in the direction of incidence ray.

P

Q

P’

Object shiftness =x

(D) The equivalent rerfractive index of a combination of a number of slabs for normal incidence 

is

 ti t  i i

Here,

 t i = t 1 + t 2 + ....... 

1 2

t1 t2

ti t t  1  2   i 1  2

www.physicsashok.in

4

OPTICS (e) The apparent depth due to a number of media is 

i

ti . i

 r

(f) The lateral shifting due to a slab is d = t sec r sin (i – r).

t d

3.

Rarer 1

(a) Cricital angle : When a ray passes from denser medium (  2 ) 90°

to rarer medium ( 1 ), then for 90° angle of refraction, the corresponding angle of incidence is critical angle. Mathematically,

Rarer medium (1)

(B) (i) When angle of incidence is lesser than critical angle, refraction takes place. the corresponding deviation is     sin 1 2 sin i   i for i = C   1  (ii) When angle of incidence is greater than critical angle, total internal reflection takes place. the corresponding deviation is

    2i

4.

Denser 2

c

 sin C  1 2

when i > C

r

i

c

i cosec 2 (f) For limiting angle of prism, i = i’ = 90°, the limiting angle of prism = 2C where C is critical angle. If angle of prism exceeds the limiting values, then the rays are totally reflected. (g)   i graph for prism: (h) For minimum deviation,

(i) i = i’ and r = r’

 A sin  m  2   (ii)   A sin 2

n

n’

i r

r’

B

i’

C

 m i

www.physicsashok.in

5

OPTICS In the case of minimum deviation, ray is passing through prism symmetrically. (i) For maximum deviation max  . i = 90° or i’ = 90° (j) For thin prism,     1 A (k) Angular dispersion, D     r  A





(l) Angular deviation,  y   y  1 A     r  (m) dispersive power =      1  y

   

    r   (n)  y   2  

B

2

1

(o) For dispersion without deviation,   y  0 (p) For deviation without dispersion,  D  0 Refractive surface formula,

x’

A

O

x

C

 2  1  2  1    u r Here,  = image distance, u = object distance, r = radius of curvature of spherical surface (a) For plane surface, r =  (B) Transverse magnification,

m

Im age size 1   object size  2u

(C) Refractive surface formula is only applicable for paraxial ray.

LENS 1.

1 1 1    u 

Lens formula :

(a) Lens formula is only applicable for thin lens. (B) r = 2  formula is not applicable for lens. (C) m 

image size   object size u

(D) Magnification formula is only applicable when object is perpendicualr to optical axis. (e) Lens formula and the magnification formula is only applicable when medium on both sides of lenses are same.

f(+ve)

(f)

f(+ve) (i)

f(-ve) (ii)

f(-ve)

f(-ve) (iii)

(iv)

f(+ve)

(v)

(g) This lens formula is applicable for converging as well diverging lens. Thin lens maker’s formula :

(vi) 1

2

1

1   2  1   1 1        1   r1 r2 

www.physicsashok.in

6

OPTICS 2.

(a) Thin lens formula is only applicable for paraxial ray. (B) This formula is only applicable when medium on both sides of lens are same. (C) Intensity is proportional to square of aperture. (D) When lens is placed in a medium whose refractive index is greater than that of lens. i.e.,

1   2 . Then converging lens behaves as diverging lens and vice versa. (e) When medium on both sides of lens are not same. Then both focal lengths are not same to each other. (f) If a lens is cut along the diameter, focal length does not change.

(g) If lens is cut by a vertical, it converts into two lenses of different focal lengths.

+

1 1 1    1  2

i.e.,

f1 f

f2

1 2 3 + + + + + + 4

(h) If a lens is made of a number of layers of different refractive index (shown in figure). Then number of images of an object formed by the lens is equal to number of different media.

5 6

(i) The minimum distance between real object and image in is 4  .

f1

(j) The equivalent focal elngth of co-axial combination of two lenses is given by 1 1 1 d    F 1  2 1  2

f2 d m 2). (A)  

x m1  m 2

(B) m 1 m 2 = 1

(C)  

D2  x 2 4D

(D) all the above

www.physicsashok.in

12

OPTICS 26. A liquid of refractive index 1.33 is placed between two identical plano-convex lenses, with refractive index 1.50. Two possible arrangement P and Q are shown. The system is (A) divergent in P, convergent in Q. (B) convergent in P, divergent in Q. (C) convergent in both (D) divergent in both.

Q

P

27. A lens of refractive index  is put in a liquid of refractive index  . If the focal length of the lens in air is

 , its focal length in liquid will be (A)

     (B)    1

    1   

   1 (C)     

(D)

  

  

28. A convergent lens is placed inside a cell filled with a liquid. The lens has a focal length +20 cm when in air and its material has a refractive index 1.50. If the liquid has a refractive index 1.60, the focal length of the system (A) –160 cm (B) – 24 cm (D) –80 cm (D) + 80 cm 29. A double convex lens, made of glass of refractive index 1.5, has focal length 6 cm. The radius of curvature of one surface is double than that of other surface. The small radius of curvature has value (A) 4.5 cm (B) 6 cm (C) 4 cm (D) 9 cm 30. If the distance between a projector and screen is increased by 1%, then illumination on the screen decreases by (A) 1 % (B) 2 % (C) 3 % (D) 4 %

31. A lens forms a sharp image of a real object on a screen. On inserting a parallel slide between the lens and the screen with its thickness along the principal axis of the lens it is found necessary to shift the screen parallel to itself ‘d’ away from the lens for getting image sharply focused on it. If the refractive index of the glass relative to air is  , the thickness of slab is (A)

d 

(B)  d

(C)

d  1

(D)   1

d 

32. A thin convex lens in used to form a real image of a bright point object. The apeture of the lens is small. A graph, shown is obtained by plotting a suitable parameter Y against another suitable parameter x. If

 = the focal length of the lens u = object distance v = image distance and Real Positive Convention is used then (A) (uV)  x; (u + V)  y (B) (u + V)  x; (uV)  y 1 u 1 (C) u  x; (D)  y  x;  y u v v

Y O

 X

-1

www.physicsashok.in

13

OPTICS 33. Which of the following best represents object distance u vs image distance v graph for a convex lens. y y y y

(A)

(B)

(C)



(D)







34. Three thin prisms are combined as shown in figure. The refractive indices of the crown glass for red, yellow and violet rays are  r,  y and  v respectively and those for the flint glass are  ’r,  ’y and  ’v respectively. The ratio A’/A for which there is no net angular dispersion.





2 y  1 (A)

 

y  1

 

 y  1  y (C)   1  y y

 y   y (B) 2   y y

2  y .  y (D)    y y

35. A point object is placed at distance of 0.3 m from a convex lens of focal length 0.2 m cut into two equal halves, each of which is displaced by 0.0005 m, as shown in figure. If C1 and C2 be their optical centres then, (A) an image is formed at a distance of 0.6 m from C1 or C2 along principal axis.

C1 O

(B)

two images are formed, one at a distance of 0.6 m and other at a distance of 1.2 m from C1 or C2 along principal axis.

(C) (D)

an image is formed at a distance of 0.12 m from C1 or C2 along principal axis. two images are formed at a distance of 0.6 m from C1 or C2 along principal axis

C2

at a separation of 0.003 m.

36.

A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3). A light beam incident normally on the face AB is totally reflected to reach on the face BC if (1983) A B 

(A) sin   37.

8 9

(B)

2 8 sin   3 9

(C) sin  

2 3

A ray of light from a denser medium strike a rarer medium at an angle of incidence i (see Figure). The reflected and refracted rays make an angle of 90° with each other. The angles of reflection and refraction are r and r’ The critical angle is r

i

r'

(A) sin

1

 tan r 

(B) sin

1

 tan i 

(C) sin

1

 tan r 

(D) tan

www.physicsashok.in

1

 sin i  14

OPTICS 38.

Two coherent monochromatic light beams of intensities  and 4  are superposed. The maximum and minimum possible intensities in the resulting beam are (A) 5  and  (B) 5  and 3  (C) 9  and  (D) 9  and 3 

39.

An isosceles prism of angle 120° has a refractive index 1.44. The parallel monochromatic rays enter the prism parallel to each other in air as shown. The rays emerge from the opposite faces

120°

(A) are parallel to each other (B) are diverging (C) make an angle 2 [sin–1 (0.72) – 30°] with each other (D) make an angle 2 sin–1 (0.72) with each other 40.

A diminished image of an object is to be obtained on a screen 1.0 m from it. This can be achieved by appropriately placing (A) a concave mirror of suitable focal length (B) a convex mirror of suitable focal length (C) a convex lens of focal length less than 0.25 m (D) a concave lens of suitable focal length

41.

A concave lens of glass, refractive index 1.5 has both surfaces of same radius of curvature R. On immersion in a medium of refractive index 1.75, it will behave as a (A) convergent lens of focal length 3.5 R (B) convergent lens of focal length 3.0 R (C) divergent lens of focal length 3.5 R (D) divergent lens of focal length 3.0 R

42.

A hollow double concave lens is made of very thin transparent material. It can be filled with air or either of two liquids L1 and L2 having refractive indices

1 and  2 respectively   2  1  1 . the lens will

diverge a parallel beam of light if it is filled with (A) air and placed in air (B) air and immersed in L1 (C) L1 and immersed in L2 (D) L2 and immersed in L1 43.

A diverging beam of light from a point source Is having divergence angle  , falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is t and the refractive index n, then the divergence angle of the emergent beam is

(A) zero

44.

(B)

1

1  n

(C) sin 



(D) 2sin

1

1   n

A ray of light passes through four transparent media with refractive indices

1 , 2 , 3 and 4 as

shown in the figure. the surfaces of all media are parallel. If the emergent ray CD is parallel to the incident ray AB, we must have

(A)

1  2

(B)

 2  3

(C)

3  4

(D)

 4  1

www.physicsashok.in

15

OPTICS 45.

A given ray of light suffers minimum deviation in an equilateral prism p, Additional prism Q and R of identical shape and of the same material as P are now added as shown in the figure. The ray will now suffer

P

(A) greater deviation (C) same deviation as before 46.

R

(B) no deviation (D) total internal reflection

Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of the surfaces of the lenses are as given in the diagrams. (A) R1

47.

Q

R2

(B) R

(C) R

R

(D) R

Two plane mirrors A and B are aligned parallel to each other, as shown in the figure A light ray is incident at an angle 30° at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is

(A) 28

(B) 30

(C) 32

(D) 34

48.

The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 2 0 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image. (A) 1.25 cm (B) 2.5 cm (C) 1.05 cm (D) 2 cm

49.

A ray of light is incident at the glass-water interface at an angle i, it emerges finally parallel to the surface of water, then the value of

(A)  4 3 sin i 50.

(B)

1 sin i

 g would be

(C)

43

(D) 1

A beam of white light is incident on glass air interface from glass to air such that green light just suffers total internal reflection. The colors of the light which will come out to air are (A) Violet, Indigo, Blue (B) All colors except green (C) Yellow, Orange, Red (D) White light

www.physicsashok.in

16

OPTICS 51.

An equilateral prism is placed on a horizontal surface. A ray pQ is incident onto it. For minimum deviation R S

Q P

(A) PQ is horizontal (C) RS is horizontal

(B) QR is horizontal (D) Any one will be horizontal

52.

A source emits sound of frequency 600 Hz inside water. The frequency heard in air will be equal to (velocity of sound in water = 1500 m/s, velocity of sound in air = 300 m/s) (A) 3000 Hz (B) 120 Hz (C) 600 Hz (D) 6000 Hz

53.

A point object is placed at the centre of a glass sphere of radius 6 cm and refractive index 1.5. The distance of virtual image from the surface is (A) 6 cm (B) 4 cm (C) 12 cm (D) 9 cm

54.

A convex lens is in contact with concave lens. the magnitude of the ratio of their focal length is

2 3.

Their equivalent focal length is 30 cm. What are their individual focal lengths? (A) –15, 10 (B) –10, 15 (C) 75, 50 (D) –75, 50 55.

A container is filled with water

   1.33 upto a height

of 33.25 cm. A concave mirror is placed 15 cm above the water level and the image of an object placed at the bottom is formed 25 cm below the water level. Focal length of the mirror is (A) 15 cm (B) 20 cm (C) –18, 31 cm (D) 10 cm

Multiple Choice Question with ONE or MORE THAN ONE correct answer: 56.

A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm. The power of the combination is (A) –1.5 dioptres (B) –6.5 dioptres (C) +6.5 diopres (D) +6.67 dioptres

57.

A converging lens is used to form an image on a screen. When the upper half of the lens is covered by an opaque screen (A) half the image will disappear (B) complete image will be formed (C) intensity of the image will increase (D) intensity of the image will decrease.

58.

A short linear object of length b lies along the axis of a concave mirror of focal length f at a distance u from the pole of the mirror. The size of the image is approximately equal to 12

u f  (A) b    f  59.

12

 f  (B) b   u f 

u f  (C) b    f 

 f  (D) b   u f 

2

A beam of light consisting of red, green and blue colours is incident on a right angled prism, figure. The refractive indices of the material of the prism for the above red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively. The prism will

www.physicsashok.in

17

OPTICS

45°

(A) separate part of the red colour from the green and blue colours (B) separate part of the blue colour from the red and green colours (C) separate all the three colours from one another. (D) not separate even partially any colour from the other two colours. 60.

A thin prism P1 with angle 4° and made from glass of refractive index 1.54 is combined with another thin prism P2 made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of the prism P2 is (A) 5.33° (B) 4° (C) 3° (D) 2.6°

61.

Two thin convex lenses of focal lengths f 1 and f 2 are separated by a horizontal distance d (where

d  f1  d  f 2 ) and their centres are displaced by a vertical separation  as shown in Figure.

Taking the origin of coordinates O, at the center of the first lens the x and y coordinates of the focal point of this lens system, for a parallel beam of rays coming from the left, are given by: (A) x 

f1 f 2 ,y f1  f 2

(B) x 

f1  f 2  d   ,y f1  f 2  d f1  f 2

(C) x 

f1 f 2  d  f1  d    f1  d  ,y f1  f 2  d f1  f 2  d

(D) x 

f1 f 2  d  f1  d  ,y0 f1  f 2  d

62.

Which of the following form(s) a virtual and erect image for all positions of the object? (A) Convex lens (B) Concave lens (C) Convex mirror (D) Concave mirror.

63.

A ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of incidence of 45°. The ray just undergoes total internal reflection. If n is the refractive index of the medium with respect to air, select the possible value(s) of n from the following: (A) 1.3 (B) 1.4 (C) 1.5 (D) 1.6

64.

A concave mirror is placed on a horizontal table, with its axis directed vertically upwards. Let O be the pole of the mirror and C its centre of curvature. A point object is placed at C. It has a real image, also located at C. If the mirror is now filled with water, the image will be. (A) real, and will remain at C (B) real, and located at a point between C and  (C) virtual, and located at a point between C and O (D) real, and located at a point between C and O

www.physicsashok.in

18

OPTICS

Fill in the blanks: 1.

A light wave of frequency 5 x 1014 Hz enters a medium of refractive index 1.5, In the medium the velocity of the light wave is .................. and its wavelength is ................ (2 Marks)

2.

A convex lens A of focal length 20 cm and a concave lens B of focal length 5 cm are kept along the same axis with a distance d between them. If a parallel beam of light falling on A leaves B as a parallel beam, then d is equal to .......... cm.

3.

A monochromatic beam of light of wavelength 6000Å in vacuum enters a medium of refractive index 1.5. In the medium its wavelength is ..., its frequency is ............. (1985)

4.

In young’s double-slit experiment, the two slits act as coherent sources of equal amplitude ‘A’ and of wavelength ‘  ’. In another experiment with the same set-up the two slits are sources of equal amplitude ‘A’ and wavelength ‘  ’, but are incoherent. The ratio of the intensity of light at the midpoint of the screen in the first case to that in the second case is ................. (1986)

5.

A thin lens of refractive index 1.5 has 7a focal length of 15 cm in air. when the lens is placed in a medium of refractive index

4 , its focal length will become ........... cm. (1987) 3

6.

A point source emits sound equally in all directions in a non-absorbing medium. Two points P and Q are at a distance of 9 meters and 25 meters respectively from the source. The ratio of amplitudes of the waves at P and Q is .................... (1989)

7.

A slab of a material of refractive index 2 shown in Figure, has a curved surface APB of radius of curvature 10 cm and a plane surface CD. On the left of APB is air and on the right of CD is water with refractive indices as given in the figure.

n1=1.0

A

P

C n2=2.0 C

n3 =

4 3

O

15 cm B

D 20 cm

An object O is placed at a distance of 15 cm from the pole P as shown. The distance of the final image of O from P, as viewed from the left is ............... (1991)

8.

A thin rod of length

f is placed along the optic axis of a concave mirror of focal length f such that itss 3

image which is real elongated, just touches the rod. The magnification is ............. 9.

A ray of light undergoes deviation of 30° when incident on an equilateral prism of refractive index The angle made by the ray inside the prism with the base of the prism is .............

10.

(1991)

2.

(1992)

A light of wavelength 6000Å in air, enters a medium with refractive index 1.5. Inside the medium its frequency is ........ Hz and its wavelength is ............... Å. (1997)

www.physicsashok.in

19

OPTICS 11.

Two thin lenses, when in contact, produce a combination of power +10 diopters. When they are 0.25 m apart, the power reduces to +6 diopters. The focal length of the lenses are ...... m and .... m. (1997)

12.

A ray of light is incident normally on one of the faces of a prism of apex angle 30° and refractive index

2 . The angle of deviation of the ray is .......... degrees.

(1997)

True / False : 13.

The intensity of light at a distance ‘r’ from the axis of a long cylindrical source is inversely proportional to ‘r’. (1981)

14.

A convex lens of focal length 1 meter and a concave lens of focal length 0.25 meter are kept 0.75 meter apart. A parallel beam of light first passes through the convex lens, then through the concave lens and moves to a focus 0.5 m away from the concave lens. (1983)

15.

A beam of white light passing through a hollow prism give no spectrum.

16.

A parallel beam of white light fall on a combination of a concave and a convex lens, both of the same material. Their focal lengths are 15 cm and 30 cm respectively for the mean wavelength in white light. On the other side of the lens system, one sees coloured patterns with violet colour at the outer edge. (1988)

17.

Match List I and List II and select the correct answer using the codes given below the lists: The arrangement shows different lenses made of substance of refractive index 1.5 and kept in air. R1 = 30 cm, R2 = 60 cm. Match the focal lengths

(1983)

Table Match

Table I

I.

II.

III.

IV.

R1

R1

R1

R1

Table II R2

R2

R2

R2

(A) I-A, II-B, III-D, IV-C (C) I-D, II-C, III-A, IV-B

A.

–120 cm

B.

+40 cm

C.

–40 cm

D.

+120 cm

(B) I-C, II-A, III-B, IV-D (D) I-B, II-D, III-C, IV-A

www.physicsashok.in

20

OPTICS 18.

Table I

Table II

I.

An object is placed at focus before A. Magnification is –  a convex mirror II. An object is placed at the centre of B. Magnification is +0.5 curvature before a concave mirror III. An object is placed at focus before C. Magnification is +1 a concave mirror. IV. An object is placed at centre of curvature D. Magnification is – 1 before a convex mirror. (A) I-B, II-D, III-A, IV-E (B) I-A, II-D, III-C, IV-B (C) I-C, II-B, III-A, IV-E (D) I-B, II-E, III-D, IV-C

19.

Match the followings:

Table I

Table II

A.

Magnification m = +1

(i)

Convex mirror

B.

Magnification m  

2 3

(ii)

Plane mirror

C.

Magnification m  

3 2

(iii)

Concave mirror

(A) A  (ii) B  (iii) C  (i) (C) A  (ii) B  (i) C  (iii)

20.

(B) A  (i) B  (ii) C  (iii) (D) A  (iii) B  (ii) C  (i)

For a concave mirror of focal length 20 cm, match the followings:

Table I Objective distance A. 10 cm B. 30 cm C. 40 cm D. 50 cm (A) A  II, B  I, C  III, D  IV (C) A  I, B  IV, C  III, D  II

Table II Nature of image (i) Magnified, inverted and real (ii) Equal size, inverted and real (iii) Smaller, inverted and real (iv) Magnified, erect and virtual (B) A  IV, B  I, C  II, D  III (D) A  IV, B  I, C  III, D  II.

PASSAGE TYPE QUESTIONS THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE The ciliary muscles of eye control the curvature of the lens in the eye and hence can alter the effective focal length of the system. When the muscles are fully relaxed, the focal length is maximum. When the muscles are strained the curvature of lens increases (that means radius of curvature decreases) and focal length decreases. For a clear vision, the image must be on retina. The image distance is therefore fixed for clear vision and it equals the distance of retina from eye-lens. It is about 2.5 cm for a grownup person.

www.physicsashok.in

21

OPTICS A person can theoretically have clear vision of objects situated at any large distance from the eye. The smallest distance at which a person can ciliary muscles are most strained in this position. For an average grown-up person, minimum distance of object should be around 25 cm. A person suffering for eye defects uses spectacles (eye glass). The function of lens of spectacles is to form the image of the objects within the range in which person can see clearly. The image of the spectacle lens becomes object for eye-lens and whose image is formed on retina. The number of spectacle lens used for the remedy of eye defect is decided by the power of the lens required and the number of spectacle-lens equal to the numerical value of the power of lens with sign. For example, power of lens required is +3 D (converging lens of focal length

100 cm), then number of lens will be 3

+3. For all the calculations required you can use the lens formula and lens maker’s formula. Assume that the eye lens is equiconvex lens. Neglect the distance between eye lens and the spectacle lens. 1.

Minimum focal length of eye-lens of a normal person is (A) 25 cm

2.

(B) 2.5 cm

25 cm 9

(C)

(D)

25 cm 11

(D)

25 cm 11

Maximum focal-length of eye lens of normal person is (A) 25 cm

(B) 2.5 cm

25 cm 9

(C)

3.

A near-sighted man can clearly see object only upto a distance of 100 cm and not beyond this. The number of the spectacles lens necessary for the remedy of this defect will be (A) + 1 (B) – 1 (C) + 3 (D) – 3

4.

A far-sighted man cannot see object only upto a distance of 100 cm from his eyes. The number of the spectacles lens that will make his range of clear vision equal to an average grown up person is (A) + 1 (B) – 1 (C) + 3 (D) – 3

5.

A person who can see objects clearly from distance 10 cm to  , then we can say that the person is (A) normal sighted person (B) near-sighted person (C) far-sighted person (D) a person with exceptional eyes having no eye defect. THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE Spherical aberration in spherical mirrors is a defect which is due to dependence of focal length ' f ' on angle of incidence

' ' as shown in figure. is given by f  R

R sec  2

  Pole (P)

Principal axis

C

F f

where R is radius of curvature of mirror and  is the angle of incidence. The rays which are closed to principal axis are called paraxial rays and the rays far away from principal axis are called marginal rays. As a result of above dependence different rays are brought to focus at different points and the image of a point object is not a point.

www.physicsashok.in

22

OPTICS 6.

If f p and f m represent the focal length of paraxial and marginal rays respectively, then correct relationship is: (A) f p  f m

7.

(B) f p  f m

(C) f p  f m

(D) None

If angle of incidence is 60°, then focal length of this rays is: (A) R

(B)

R 2

(C) 2R

(D) 0

8.

The total deviation suffered by the ray falling on mirror at an angle of incidence equal to 60° is: (A) 180° (B) 90° (C) Can’t be determined (D) None

9.

For paraxial rays, focal length approximately is: (A) R

10.

(B)

R 2

(C) 2R

(D) None

Which of the following statements are correct regarding spherical aberration: (A) It can be completely eliminated (B) it can’t be completely eliminated but is can’t be minimised by allowing either paraxial or marginal rays to hit the mirror (C) It is reduced by taking large aperture mirrors (D) None THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE Rainbow is formed during rainy season due to refraction and total internal reflection of rays falling on suspended water droplets. When rays of the sun fall on rain drops, the rain drops disperse the light and deviate the different colours by refraction and total internal reflection to the eye of the observer. A person observing the drops will see different colours of the spectrum at different angles. The rainbow which results from single total internal reflection is called primary rainbow and secondary rainbow is formed due to two total internal reflections suffered by rays falling on water drops.

Rays from sun

A V

C R

Re d

D l et vio

11.

12.

Secondary rainbow

R Re d

v io le t

B

V

Primary rainbow

Figure shows formation of rainbow due to four drops A, B, C and D. The light surffers only one total linternal reflection in drops C and D forming primary rainbow. Secondary rainbow is formed by drops A and B where light suffers two total linternal reflections. Rainbow is an arc of: (A) Circle (B) Ellipse (C) Parabola (D) Can’t be determined The visibility of the rainbow is due to: (A) All rays (B) Rays undergoing maximum deviation (C) Rays undergoing minimum deviation (D) None

www.physicsashok.in

23

OPTICS 13.

14.

15.

In primary rainbow, the colour of outer edge is: (A) Blue (B) Violet (C) Red

(D) None

In secondary rainbow, the colour of inner edge is: (A) Red (B) Violet (C) Indigo

(D) None

The necessary condition for the observer to see rainbow is: (A) Sun, observer’s eye and the centre of the rainbow arc lie on the same line (B) Sun, observer’s eye and the centre of the rainbow arc lie on the different line (C) From any position provided sun is at the back of the observer (D) None THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE The laws governing the behavior of the rays namely rectilinear propagation, laws of reflection and refraction can be summarised in one fundamental also known as Fermat’s principle. According to this principle a ray of light travels from one point to another such that the time taken is at a stationary value (maximum or minimum). If c is the velocity of light in a vacuum, the velocity in a medium of refractive index n is

c nl , hence time taken to travel a distance l is . If the light passes through a number of n c

1 1  nl and  n dl . If refractive index varies continuously. Now,, nl c c

media, the total time taken is 

is the total optical path, so that Fermat’s principle states that the path of a ray is such that the optical path in at a stationary value. This principle is obviously in agreement with the fact that the ray are straight lines in a homogenous isotropic medium. It is found that it also agrees with the classical laws of reflection and refraction. 16.

If refractive index of a slab varies as

  1  x 2 where x is measured from one end, then optical path

length of a slab of thickness 1 m is: (A) 17.

4 m 3

(B)

3 m 4

(C) 1 m

(D) None

The optical path length followed by ray from point A to B given that laws of reflection are obeyed as shown in figure is: A

B

P (A) Maximum 18.

(B) Minimum

(C) Constant

(D) None

The optical path length followed by ray from point A to B given that laws of reflection are obeyed as shown in figure is A

(A) Maximum

(B) Minimum

B

(C) Constant

(D) None

www.physicsashok.in

24

OPTICS 19.

The optical path length followed by ray from point A to B given that laws of refraction are obeyed as shown in figure is A

B (A) Maximum 20.

(B) Minimum

(C) Constant

(D) None

The optical path length followed by ray from point A to B given that laws of refraction are obeyed as shown in figure is

A B A and B are focii of ellipse (A) Maximum

(B) Minimum

(C) Constant

(D) None

THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE One hard and stormy night you find yourself lost in the forest when you come upon a small hut. Entering it you see a crooked old woman in the corner hunched over a crystal ball. You are about to make a hasty exit when you hear the howl of wolves outside. Taking another look at the gypsy you decide to take your chances with the wolves, but the door is jammed shut. Resigned to bad situation your approach her slowly, wondering just what is the focal length of that nifty crystal ball. 21.

If the crystal ball is 20 cm in diameter with R.I. = 1.5, the gypsy lady is 1.2 m from the central of ball, where is the image of the gypsy in focus as you walk towards her? (A) 6.9 cm from the crystal ball (B) 7.9 cm from the crystal ball (C) 8.9 cm from the crystal ball (D) None

22.

The image of old lady is: (A) real, inverted an enlarged (C) erect, virtual and magnified

23.

(B) erect, virtual and small (D) real, inverted and diminished

The old lady moves the crystal ball closer to her wrinkled old face. At some point you can no longer get an image of her. At what object distance will there be no change of the gypsy formed? (A) 10 cm (B) 5 cm (C) 15 cm (D) None

THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE The table below contains some physical properties of common optical materials. The refractive index of a material is a measure of the amount by which light is bent upon entering the material. The transmittance range is the range of wavelengths over which the material is transparent.

www.physicsashok.in

25

OPTICS

Material

Lithium fluoride Calcium fluoride Sodium chloride Quartz Potassium bromide Flint glass* Cesium iodide

Physical Properties of Optical Materials Refractive Transmittance Useful range index for light for prisms range (m) of 0.589 m (m) 1.39 0.12-6 2.7-5.5

Chemical resistance Poor

1.43

0.12-12

5-9.4

Good

1.54

0.3-17

8—16

Poor

1.54 1.56

0.20-3.3 0.3-29

0.20-2.7 15—28

Excellent Poor

1.66 0.35—2.2 0.35-2 1.79 0.3—7.0 15-55 *Flint glass is lead oxide doped quartz.

Excellent Poor

24.

According to the table, which material(s) will transmit light at 25  m – (A) Potassium bromide only (B) Potassium bromide and cesium iodide (C) Lithium fluoride and cesium iodide (D) Lithium fluoride and flint glass

25.

A scientist hypothesizes that any material with poor chemical resistance would have a transmittance range wider than 10  m . The properties of which of the following materials contradicts this hypothesis– (A) Lithium fluoride (B) Flint glass (C) Cesium iodide (D) Quartz

26.

When light travels from one medium to another, total internal reflection can occur if the first medium has a higher refractive index than the second. Total internal reflection could occur if light were travelling from– (A) Lithium fluoride of flint glass (B) potassium bromide to cesium iodide (C) quartz to potassium bromide (D) flint glass to calcium fluoride

27.

Based on the information in the table, how is the transmittance range related to the useful prism range– (A) The transmittance range is always narrower than the useful prism range (B) The transmittance range is narrower than or equal tot he useful prism range (C) The tranmittance range increases as the useful prism range decreases (D) The tranmittance range is wider than and includes within it the useful prism range

28.

The addition of lead oxide to pure quartz has the effect of– (A) decreasing the transmittance range and the refractive index (B) decreasing the transmittance range and increasing the refractive index (C) increasing the transmittance range and the useful prism range (D) increasing the transmittance range and decreasing the useful prism range. THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE A periscope viewing system is to be used to observe the behavior of primates in a large environmentally controlled room on the upper floor of a large research facility. The periscope, like those used on

www.physicsashok.in

26

OPTICS submarines, is essentially a large, folded-path, low power telescope (using prisms to fold the light path). A sketch of the preliminary design appears below. Like all Newtonian telescopes, it uses a relatively long focal length objective lens to form a real image in front of the eyepiece lens (of shorter focal length). The observer looks through the eyepiece lens to see the final image, in the same manner that one would use a magnifying glass.

The distance between the lenses is approximately equal to the sum of their focal lengths. The eyepiece, in this design, can be moved forward or back in order to focus on the primates as they move closer to or further away from the objective lens. 29.

The total tube length of the three sections is to be 4 m. The objective lens available has a focal length of 3 m. What should the focal length of the eyepiece lens be? (A) 0.75 m (B) 1 m (C) 1.33 m (D) 7 m

30.

A visitor seeing the sketch points out an important flaw that will require a design change. what is the flaw? (A) The focal length of the eyepiece lens is too short. (B) The images of the primates will be inverted (C) The objective lens should be a diverging lens. (D) The prisms cannot be used in this way.

31.

A visitor seeing the sketch points out an important flaw that will require a design change. What is the flaw? (A) The focal length of the eyepiece lens is too short. (B) The images of the primates will be inverted (C) The objective lens should be a diverging lens. (D) The prisms cannot be used in this way.

32.

What will be the approximate magnification of this periscope? (A) 0.67x (B) 1x (C) 3x (D) 300x

33.

The prisms (45–45–90° prisms) turn the light path through 90° by “total internal reflection” from the inside hypotenuse faces of the prisms when the incident angle is 45° as in the sketch. Can one use crown glass with an index of refraction of 1.52 for the prism? (A) yes, because the critical angle for crown glass is 47° (B) yes, because the critical angle for crown glass is 41°. (C) No, because the critical angle for crown glass is exactly 47° (D) No, because the critical angle for crown glass is exactly 41°.

34.

Describe the properties of the image that one sees with this preliminary design (A) real, inverted, magnified (B) real, upright, magnified (C) virtual, upright, same size as object. (D) virtual, inverted, magnified

35.

The telescope is focused on a primate rather far away on the farside of the large habitat. As the primate moves rather closer to the telescope, what must the observer do to see the primate clearly? (A) No change, the image remains clear. (B) Move the eyepiece away from the objective. (C) Move the eyepiece closer to the objective. (D) Use an inverting eyepiece because the image flips.

www.physicsashok.in

27

OPTICS THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE In the normal human eye, light from an object is refracted by the cornea-lens system at the front of the eye and produces a real image on the retina at the rear of the eye. For a given eye, its lens-to-retina distance is fixed at about 2.5 cm. Most of the focusing of an image is done by the cornea, which has a fixed curvature that is convex with respect to incoming light. The importance of the lens is that its radius of curvature ccan be changed, allowing the lens to fine-tune the focus. The lens is surrounded by the ciliary muscle. Contraction of the muscle decreases tension on the lens. This allows the natural elasticity of the lens to produce an increase in the radius of curvature. when the muscle relaxes, the lens flattens out, decreasing tis radius of curvature. Unfortunately, the lens losses elasticity with age and the ability to alter curvature decreases. The range over which clear vision is possible is bounded by the far point and the near point. In normal vision the far point is infinity and the near point depends on the radius of curvature of the lens. For normal eyes the average near point for reading is 25 cm.

AGE, years 10 20 30 40 50 60

NEAR POINT, cm 7 10 14 22 40 200

In the myopic (nearsighted) eye, the lens-to-retina length is too long and/or the radius of curvature of the cornea is too great. This causes rays from an object at infinity to focus at a point in front of the retina. The far point is closer than normal .A corrective lens will put a virtual image of a distant object at the position of the actual far point of the eye. In the hyperopic (farsighted) eye, the lens-to-retina length is too short and/or the radius of curvature of the cornea is not great enough. This causes rays from an object at infinity to focus at a point behind the retina. The near point is farther away than normal. A corrective lens will put a virtual image of the close object at the position of the actual near point. The relation among the object (o) and image (i) distances from the eye and the focal length (f) of the lens is given by the lens-distance rule :

1 o 1 i  1 f .

When using this equation, all distances are given in centimeters. The power of corrective lenses is usually given in units called diopters. Power, in diopters, is the reciprocal of the focal length in meters : Pdiopter  1 f meter . By convection – I. Converging lenses have positive focal lengths, and diverging lenses have negative focal lengths. II. Real images have positive distances from the lens, and virtual images have negative distances from the lens. 36.

The lens system of the myopic eye is best described as – (A) producing too much convergence. (B) producing too little convergence. (C) producing too much divergence. (D) producing too little divergence.

37.

An optometrist examined John’s eyes. The farthest object he can clearly focus on with his right eye is 50 cm away. What is the power of the contact lens required to correct the vision in his right eye – (A) –0.50 diopters (B) –2.0 diopters (C) +2.0 diopters (D) +5.0 diopters

www.physicsashok.in

28

OPTICS 38.

In a mildly hyperopic eye, the focal length of the eye’s natural lens can be corrected by – (A) contracting the muscle and increasing the radius of curvature. (B) contracting the ciliary muscle and decreasing the radius of curvature (C) relaxing the ciliary muscle and increasing the radius of curvature. (D) relaxing the ciliary muscles and decreasing the radius of curvature.

39.

Jane must wear a contact lens with a power of +3.00 diopters in one eye to be able to clearly focus on an object 2.5 cm in front of the eye. Based on the vision in this eye, which of the following is the most likely age range for Jane – (A) Less than 40 years old (B) From 40 to 49 years old (C) From 50 to 59 years old (D) 60 years or older

40.

George wears eyeglasses that sit 2.0 cm in front of his eyes. His incorrect far point is 50 cm. What is the focal lengths of his eyeglasses – (A) –50 cm (B) +50 cm (C) –48 cm (D) +48 cm

41.

In a surgical procedure called radial keratotomy, (RK), a laser is used to flatten the cornea by placing as series of hairline cuts around the perimeter of the cornea. Which statement is most accurate – (A) RK corrects myopia by decreasing the focal length of the eye. (B) RK corrects myopia by increasing the focal length of the eye. (C) RK corrects hyperopia by decreasing the focal length of the eye. (D) RK corrects hyperopia by increasing the focal length of the eye. THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE Student are given a variety of lenses and optics equipment, such as lens holders, lighted object sources. Optical benches, meter sticks and tapes, image screens, and several examples of commercial optical equipment, such as microscopes and telescopes. They are to work in an open-ended optics lab in order to learn the general principles of lenses and the optical devices that can be constructed using lenses.

42.

A student is given a short focal length converging lens and long focal length converging lens. One lens is placed in a holder. A lighted object is placed 18 cm in front of the lens and it is found that a clear image can be focused on a screen placed 36 cm behind the lens. what is the focal length of this lens? (A) 8 cm (B) 12 cm (C) 27 cm (D) 46 cm

43.

What magnification is produced by the above lens when the object is 18 cm in front of the lens and the image is 36 cm behind the lens? (A) 2x (B) 3x (C) 4x (D) 6x

44.

A lighted object is placed 6 cm in front of the second lens, which has a focal length of +24 cm. Where is the image and which kind of image is it? (A) 8 cm in front of the lens: a virtual image. (B) 8 cm behind the lens: a real image (C) 16 cm in front of the lens: a real image (D) 16 cm behind the lens; a virtual image.

45.

The 24 cm focal length lens is used as the objective of a simple refracting telescope and a third converging lens of focal length +8 cm is used as the eyepiece. What is the magnification of this simple refractor? (A) 0.6x (B) 3x (C) 4x (D) 6x

46.

A commercial microscope is examined by the student. The objective is marked 20x and the eyepiece is marked 10x. what power objective should replace the above objective so that the microscope’s magnification will be 400x (A) 5x (B) 10x (C) 40x (D) 100x

www.physicsashok.in

29

OPTICS 47.

A lighted object is placed 24 cm in front of a +12 cm focal lengths lens. The image formed by this lens is the object for a second lens of +24 cm focal length. The second lens is placed 72 cm behind the first lens. where is the final image with respect to the second lens? (A) 24 cm in front of # 2 (B) 24 cm behind # 2 (C) 36 cm in front of # 2 (D) 48 cm behind # 2

48.

A lens of focal length +24 cm is used to view an object placed 12 cm in front of the lens. The object is 5 cm tall. How tall is the image? (A) 2.5 cm (B) 3.3 cm (C) 7.5 cm (D) 10 cm

49.

A diverging lens of focal length –24 cm is now used with the object 12 cm in front of the lens. How tall is the image if the object is 5 cm tall? (A) 2.5 cm (B) 3.3 cm (C) 8 cm (D) 10 cm

50.

A near sighted student cannot see objects clearly unless they are as close as 80 cm (his “far-point”). The image that he sees through his new contact lens is a virtual image because he looks through the lens to see the image. what focal length lenses does he need in order to see very distance objects, such as the starts? (A) –20 cm (B) –30 cm (C) –4 cm (D) – 25 cm THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE The phenomenon of refraction has long intrigued scientists and was actually used to corroborate one of the major mysteries of early science: the determination of the speed of light. The refractive index of a transparent material irrelated to a number of the physical properties of light. In terms of velocity, the refractive index represents the ratio of the velocity of light in a vacuum to its velocity in the material. From this ratio, it can be seen that light is retarded when it passes through most types of matter. It is worth noting that prisms break up white light into the seven “colors of the rainbow” because each color has a slightly different velocity in the medium. Snell’s law allows one to follow the behavior of light in terms of its path when moving from a material of one refractive index to another with the same, or different refractive index. It is given by:

n1 sin 1  n2 sin  2 , where “I” refers to the first medium through which the ray passes, “2” refers to the second medium, and the angles refer to the angle of incidence in the first medium of refraction in the second

1  and the angle

 2  .

A ship went out on a search for a sunken treasure chest. In order to locate the chest, they shone a beam of light down into the water using a high intensity white light source as shown in Figure. The refractive index for sea water is 1.33 while that for air is 1.00. 51.

From the information in the passage, how would you expect the speed of light in air to compare with the speed of light in a vacuum (which is given by “c”)? (A) It would be the same (=c) (B) It would be greater than c. (C) It would be less than c. (D) This cannot be determined from the information given.

www.physicsashok.in

30

OPTICS 52.

Using the information in the passage, what must the approximate value of chest as shown in Figure? (A) 15.2° (B) 30.4°

53.

(C) 45.6°

2 be such that it hit the

(D) 63.4°

How does the refractive index in water light compare with that of red light given that violet light travels more slowly in water than red light? (A) nviolet  nred

(B) nviolet  nred

(C) nviolet  nred

(D) This depends on the relative speeds of the different colors in a vacuum.

54.

Total internal reflection first occurs when a beam of light travels from one medium to another medium which has a smaller refractive index at such an angle of incidence that the angle of refraction is 90°. This angle of incidence is called the critical angle. What is the value of the sine of this angle when the ray moves from water towards air? (A) 2 (B) 0.75 (C) 0.50 (D) 0

55.

What would happen to the critical angle, in the previous question, if the beam of light was travelling from water to a substance with a greater refractive index than air, but a lower refractive index than water? (A) It would increase (B) It would decrease (C) It would remain the same (D) Total internal reflection would not be possible.

56.

Which of the following would you expect to remain constant when light travels from one medium to another and the media differ in their refractive indices? (A) Velocity (B) Frequency (C) Wavelength (D) Intensity. THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE The invention of the compound microscope by Jansen in the late 1500’s truly revolutionized the world of science, particularly the field of cellular and molecular biology. The discovery of the cell as the fundamental unit of living organisms and the insight into the bacterial world are two of the contributions of this instrument to science. It is unseemly that such a relatively simplistic apparantus took generations to be developed. Its main component are two convex lenses: one acts as the main magnifying lens and is referred to as the objective, and another lens called the eyepiece. The two lenses act independently of each other when bending light rays. The actual lens set-up depicted in Figure.

Light from the object (O) first passes thought he objective and an enlarged, inverted first image is formed. The eyepiece then magnifies this image. Usually the magnification of the eyepiece is fixed (either x 10 or x 10) and three rotating objective lenses are used : x 10, x 40 and x 60. The most recent development in microscope technology is the electron microscope which uses a beam of electrons instead of light. Photographic film must be used otherwise no image would be formed on the retina. This microscope has a resolution about a hundred times that of the light microscope. 57.

Based on the passage, what type of image would have to be produced by the objective magnification? (A) Either virtual or real (B) Virtual (C) Real (D) It depends on the focal length of the lens.

www.physicsashok.in

31

OPTICS 58.

Where would the first image have to be produced by the objective relative to the eyepiece such that a second, enlarged image would be generated on the same side of the eyepiece as the first image (first image distance = d1)? (A) di  Fe

(B) di  Fe

(C) 2  Fe  d i  Fe

(D) di  2  Fe

59.

Two compound microscopes A and B were compared. Both had objectives and eyepieces with the same magnification but A gave an overall magnification that was greater than that of B. Which of the following is a plausible explanation? (A) The distance between objective and eyepiece in A is greater than the corresponding distance in B. (B) The distance between objective and eyepiece in A is less than the corresponding distance is B. (C) The eyepiece and objective positions were reversed in A. (D) The eyepiece and objective positions were reversed in B.

60.

A student attempted to make a compound microscope. However, when she tried to view an object through the apparatus, no image was seen. Which of the following could explain the mishap? I. The object distance = focal length of objective. II. The object distance for eyepiece lens as her eyepiece. III. The student used a diverging lens as her eyepiece. IV. The student used a converging lens as her objective (A) I, II, III and IV (B) I, II, III (C) I, II, IV (D) II, III, IV

61.

The magnification of the eyepiece of a compound microscope is x15. The image height is 25 mm and the magnification of the objective is x40. What is the object height? (A) 1.67 mm (B) 0.60 mm (C) 0.38 mm (D) 0.04 mm

62.

What is the refractive power of an objective lens with a focal length of 0.50 cm? (A) 0.2 diopters (B) 2.0 diopters (C) 20 diopters (D) 200

THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE Magnification by a lens of an object at distance 10 cm from it is –2. Now a second lens is placed exactly at the same position where first was kept, without changing the distance object and lens. The magnification by this second lens is – 3. 63.

Now both the lenses are kept in contact at the same place. What will be the new magnification. (A) 

64.

13 5

(B) 

12 7

(C) 

6 11

(D) 

5 7

What is the focal length of the combination when both lenses are in contact. (A)

60 cm 17

(B)

5 cm 17

(C)

12 cm 7

(D)

13 cm 9

THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE In the case of convex lens, when object is moved from f to 2f, its image is real, inverted and magnified. It moves from f to infinity on other side. 65.

Focal length of a convex lens is 10 cm. When the object is moved from 15 cm to 25 cm, the magnitude of linear magnifications. (A) will increase (B) will decrease (C) will first increase then decrease (D) will first decrease than increase.

www.physicsashok.in

32

OPTICS 66.

Image of object AB shown in figure will be like: B 2F

A

F

A' (A)

F

A'

(B)

2F

F

2F

B' A'

(C)

F

A'

(D)

2F

B'

F

2F

B'

B'

THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE Figure shows a simplified model of the eye that is based on the assumption that all of the refraction of entering light occurs at the cornea. The cornea is a converging lens located at the outer surface of the eye with fixed focal length approximately equal to 2 cm. Parallel light rays coming from a very distant object are refracted by the cornea to produce a focused image on the retina. The retina then transmits electrical impulse along the optic nerve to the brain. cornea retina

Two common defects of vision are myopia and hyperopia. Myopia, sometimes referred to as nearsightedness, occurs when the cornea focuses the image of a distance object in front of the retina. Hyperopia, sometimes referred to as farsightedness, occurs when the cornea focuses the image of a nearby object behind the retina. Both of these problems can be corrected by introducing another lens in front of the eye so that the two lens system produces a focused image on the retina. If an object is so far away from the lens system that its distance may be taken as infinite, then the following relationship holds:

1 1 1   , where f is the focal length of the cornea, f , is the focal length of the correcting c l f c fl  x v

lens, x is the distance from the correcting lens to the cornea, and v is the image distance measured from the cornea. (Note : The index of refraction is 1.0 for air and 1.5 for glass). 67.

How far away should the retina be from the cornea for normal vision? (A) 0.5 cm (B) 1.0 cm (C) 2.0 cm

(D) 4.0 cm

68.

For a distant object, the image produced by the cornea is: (A) real and inverted (B) real and upright (C) virtual and inverted (D) virtual and upright.

69.

What kind of lens would be suitable to correct myopia and hyperopia respectively? (Note : Assume that the correcting lens is at the focal point of the cornea so that x  f c .) (A) Converging, converging (C) Diverging, diverging

70.

(B) Converging, diverging (D) Diverging, converging

The focal length of a woman’s cornea is 1.8 cm, and she wears a correcting lens with a focal length of 16.5 cm at a distance x = 1.5 cm from her cornea. What is the image distance v measured from the cornea for a distant object? (A) 1.0 cm (B) 1.5 cm (C) 2.0 cm (D) 2.5 cm

www.physicsashok.in

33

OPTICS 71.

In the case of contact lens, the cornea and the correcting lens are actually touching and act together as a single lens. If the focal length of both the cornea and the contact lens are doubled, then the image distance v for a distant object would: (A) be 1/4 the old value (B) be 1/2 the old value. (C) be the same as the old value (D) be twice the old value.

Level # 2 A

1.

In what direction should a beam of light be sent from point A (Figure) contained in a mirror box for it to fall onto point B after being reflected once from all four walls? Point A and B are in one plane perpendicular to the walls of the box (i.e., in the plane of the drawing).

2.

A concave mirror has the form of a hemisphere with a radius R = 55 cm. A thin layer of an unknown transparent liquid is poured into this mirror, and it was found that the given optical system produces, with the source in a certain position two real image, one of which (formed by direct reflection) coincide with source and the other is at a distance of  = 30 cm from it. Find the refractive index  of the liquid.

3.

A point source of light S is placed on the major optical axis of concave mirror at a distance of 60 cm. At what distance from the concave mirror should a flat mirror be placed for the rays to converge again at the point S having been reflected from the concave mirror and then from the flat one? Will the position of the point where the rays meet change if they are first reflected from the flat mirror? The radius of the concave mirror is 80 cm.

4.

A pile 4 m high driven into the bottom of a lake is 1 m above the water. Determine the length of the shadow of the pile on the bottom of the lake if the sun rays make an angle of 45° with the water surface. The refractive index of water is 4/3.

5.

In figure, a fish water watches a fish through a 3.0 cm thick glass wall of a fish tank. The watcher is in level with the fish; the index of refraction of the glass is 8/5 and that of the water is 4/3.

8.0 cm

3.0 cm

B

6.8 cm

Observer Water

Wall

(a) (B)

6.

To the fish, how far away does the watcher appear to be? To the watcher, how far away does the fish appear to be?

A hollow sphere of glass of refractive index  has a small mark on its interior surface which is observed from a point outside the sphere on the side opposite the center. The inner cavity is concentric with external surface and the thickness of the glass is every where equal where equal to the radius of the

  1 R inner surface. Prove that the mark will appear nearer than it really is, by a distance 3   1 , where R is the radius of the inner surface.

www.physicsashok.in

34

OPTICS 7.

8.

Y

A long rectangular slab of transparent medium of thickness d is placed on a table with length parallel to the x-axis and width parallel to the y-axis. A ray of light is travelling along y-axis at origin. the refractive 0 index  of the medium varies as   , where  0 and 1  x r  r (> 1) are constants. The refractive index of air is 1. (a) Determine the x-coordinate of the point A, where the ray intersects the upper surface of the slab-air boundary. (B) Write down the refractive index of the medium at A. (C) Indicate the subsequent path of the ray in air.

A d medium X

O

A man of height 2.0 m is standing on level road where because of temperature variation the refractive index of air is varying as   1 ay , where y is height from road. If a = 2.0 x 10–6 m –1. Then find distant point that he can see on the road.

9.

A portion of straight glass rod of diameter 4 cm and refractive index 1.5 is bent into an arc of circle of radius R. A parallel beam of light is incident on it as shown in the figure. Find the smallest value of R which permits all the light to pass around the arc.

R

Observer

10. A glass sphere has a radius of 5.0 cm and a refractive index of 1.6. A paperweight is constructed by slicing through the sphere on a plane that is 2.0 cm from the centre of the sphere and perpendicular to a radius of the sphere that passes through the center of the circle formed by the intersection of the plane and the sphere. The paperweight is placed on a table and viewed directly above by an observer who is 8.0 cm from the table top as shown in figure. when viewed through the paperweight, how far away does the tabletop appear to the observer?

8.0 cm 3.0 cm 5. 0

cm

11. A ray of light is incident on a composite slab at a angle of incidence i as shown in the figure. Find the lateral shift x of the ray when it comes out from the otherside.

A

12. A prism of apex angle A is made up of a material of refractive index  . The refractive indices of the mediums on the left and right sides are  1 and  2 respectively. A ray of light is incident from the side of medium of refractive index  1 at an angle i and comes out from the other side as shown in the figure. Find the angle of deviation.

i

1



www.physicsashok.in

2

35

OPTICS 13. A hemisphere of radius a/2 and made up of a material of variable refractive index is placed with its base centre O at the origin as shown in the figure. a . ax A ray of light is incident at the point O at an angle  with the normal in the xy plane and comes out through a point P on its curved surface. Find the coordinate of the point P if   0 .

The refractive index of the material of the hemisphere varies as  

14. A ray of light is incident on the sphere of radius R and refractive index  as shown in the figure. The incident ray is parallel to a horizontal diameter and the distance between the incident ray and the horizontal diameter is b. Find the angle of deviation  suffered by the ray..

b R

15. An intense beam parallel to the principal axis is incident on a convex lens. Multiple extra images F 1, F 2, ...... are formed Principal due to feeble internal reflections, called flare spots as shown axis F1 in the figure. The radius of curvature of the lens is 30 cm and 60 cm and the refractive index is 1.5. Find the position of the first flare spot.

u

F2 F0

16. The image of the object shown in the figure is formed at the bottom of the tray filled with water. From the details given in the figure, calculate the value of h.  = 30 cm /4 O

36 cm

1m

85 cm

h

Y

17. In the given figure there are two thin lenses of same focal length  arranged with their principal axes inclined at an angle  . The separation between the optical centers of the lenses is 2  . A point object lies on the principal axis of the O convex lens at a large distance to the left of convex lens. (a) Find the coordinates of the final image formed by the system of lenses taking O as the origin of coordinate axes, and (B) Draw the ray diagram.



X

2

www.physicsashok.in

36

OPTICS 18. (a) A prism has refracting angle equal to  /2. It is given that  is the angle of minimum deviation and  is the deviation of the ray entering at grazing incidence. Prove that sin  = sin2  and cos  =  cos  (b) A ray of light passes through a prism in a principal plane the deviation being equal to angle of 2 incidence which is equal to 2  . It is given that  is the angle of prism. Show that cos  

1





8 2  1

where  is the refractive index of the material of prism. 19. A thin flat glass plate is placed in front of a convex mirror. At what distance b from the plate should a point source of light S be placed so that its image produced by the rays reflected from the front surface of the plate coincides with the image formed by the rays reflected from the mirror? The focal length of the mirror is  = 20 cm and the distance from the plate to the mirror a = 5 cm. How can the coincidence of the images be established by direct observation?

S

a

20. A concave mirror forms the real image of a point source lying on the optical axis at a distance of 50 cm from the mirror. The focal length of the mirror is 25 cm. The mirror is cut in two and its halves are drawn a distance of 1 cm apart in a direction perpendicular to the optical axis. How will the images formed by the halves of the mirror be arranged?

b

1 cm

21. A glass hemisphere of radius 10 cm and  = 1.5 is silvered over tis curved surface. There is an air bubble in the glass 5 cms from the plane surface along the axis. Find the position of the images of this bubble seen by observer looking along the axis into the flat surface of the hemisphere. 22. The height of a candle flame is 5 cm. A lens produces an image of this flame 15 cm high on a screen. Without touching the lens, the candle is moved over a distance of  = 1.5 cm away from the lens, and a sharp image of the flame 10 cm high is obtained again after shifting the screen. Determine the main focal length of the lens. 23. A thin converging lens of focal length  is moved between a candle and a screen. The distance between the candle and the screen is d (> 4  ). Show that for two different positions of the lens, two different images can be obtained on the screen. If the ratio of dimensions of the image is  , find the value of (  + 1/  ). 24. Three convergent thin lenses of focal lengths 4a, a and 4a respectively are placed in order along the axis so that the distance between consecutive lenses is 4a. Prove that this combination simply inverts every small object on the axis without change of magnitude or position. 25. A converging bundle of light rays in the shape in the shape of a cone with the vertex angle of 40° falls on a circular diaphragm of 20 cm diameter. A lens with a focal power of 5 diopters is fixed in the diaphragm. What will the new cone angle be? 26. A ray of light is incident on the spherical surface of radius of curvature R as shown in the figure. Therefractive index on the right side of spherical surface is  . The medium ont he left side of the spherical surface is air.. The distance of the incident ray from the axis of the spherical surface is b. After refraction the ray intersects the axis at a point. F. Find the distance  of the point F from the pole O.

www.physicsashok.in

37

OPTICS 10 cm 27. Consider an arrangement of two equibi convex lenses of focal length in air 10 cm. The refractive index of the glass of which the lenses are g between the made is  g = 3/2 and the refractive index of water filling the space two lenses is  w = 4/3. A small object O is placed on the axis O AIR at a distance of 10 cm from the first lens in air as shown in the figure. The distance of separation between the two lenses is 10 cm. Find the position and magnification of the final image.

10 cm g AIR

A

28. A thin convex lens of focal length 1m is cut into three parts A, B and C along the diameter. The thickness of the middle layer C is 1 cm. The middle layer is now removed and the two parts A nad B are put together to form a composite lens. Then the part C is also placed infront of this composite lens symmetrically as shown in the figure. A paraxial beam of light is incident along tyhe axis of the part C. Find the distance between the two images formed.

C

1 cm

B A

C

B 29. An equi biconvex lens of focal length 10 cm in AIR and made up of material of refractive index 3/2 is polished on one side. Another identical lens (not polished) is placed infront of the polished lens at a distance of 10 cm as shown in the figure. The space between the two lenses is filled with a liquid of refractive index 4/3. An object O is placed infront of the unpolished lens at a distance of 10 cm. Find the final position of the image.

10 cm

10 cm

B 60° 30. Consider an equilateral prism ABC as shown in the figure. A ray of light is incident on the face AB and gets transmitted into the prism. Then total internal reflection takes place at the face BC and the ray comes out of prism through the face AC. The total angle of deviation is 120°. Find the refractive index  of the material of the prism.

60° A

60° C

Level # 3 1.

An object is placed 21 cm in front of a concave mirror of radius of curvature 10 cm. A glass slab of thickness 3 cm and refractive index 1.5 is then placed close to the mirror in the space between the object and the mirror. Find the position of the final image formed. (You may take the distance of the near surface of the slab from the mirror to be 1 cm). [IIT 1980]

2.

The x-y plane is the boundary between two transparent media. Medium –1 with z  0 has refractive index

2 and medium –2 with z  0. 0, has a refractive index 3 . A ray of light in medium –1 given by  the vector A  6 3 ˆi  8 3 ˆj  10 kˆ is incident on the plane of separation. Find the unit vector in the direction of the refracted ray in medium – 2. [IIT 1999]

3.

An object is placed in front of a convex mirror at a distance of 50 cm. A plane mirror is introduced covering lower half of the convex mirror. If the distance between the object and the plane mirror is 30 cm, it is found that there is no parallux between the images formed by two mirrors. What is the radius of curvature of the convex mirror? [IIT 1973]

www.physicsashok.in

38

OPTICS 4.

A rectangular block of glass is placed on a printed page lying on a horizontal surface. Find the value of the refractive index of glass for which the letters on the page are not visible from any of the vertical faces of the block. [IIT 1979]

5.

A glass lens has focal length 5 cm in air. What will be its focal length in water. (Refractive index of glass is 1.51 and that of water is 1.33). [IIT 1977]

6.

A ray of light is travelling form diamond to glass. Calculate the minimum angle of incidence of the ray as the diamond glass interface such that no light is refracted into glass. W hat will happen if the angle of incidence exceeds the angle? (refractive index of glass is 1.51 and that of diamond is 2.47)[IIT 1977]

7. 8.

What is the velocity of light in glass of refractive index 1.5? (Velocity of light in air = 3 x 1010 cm/sec.) [IIT 1976] Photographs of the ground are taken from an aircraft flying at an altitude of 2000 meters by a camera with a lens of focal length 50 cm. the size of the film in the camera is 18 cm x 18 cm. What area of the ground can be photographed by this camera at any one time? [IIT 1976]

9.

A rectangular glass block of thickens 10 cm and refractive index 1.5 is placed over a small coin. A 4 to a height of 10 cm and is placed over the glass block. 3 (a) Find the apparent position of the object when it is viewed at near normal incidence. (b) Draw a neat ray diagram. (c) If the eye is slowly moved away from the normal at a certain position the object is found to disappear due to total internal reflection. At which surface does this happen and why? [IIT 1975]

beaker filled with water of refractive index

10. A ray of light travelling in air is incident at grazing angle (incident angle = 90°) on a long rectangular slab of a transparent medium of thickness t = 1.0 m (see figure). The point of incidence is the origin A (0, 0). The medium has a variable index of refraction n (y) given by n(y) = [Ky3/2 + 1] ½ –3/2 where K = 1.0 (meter) The refractive index of air is 1.0. (a) Obtain a relation between the slope of the trajectory of the ray at a point B (x, y) in the medium and the incident angle at that point. (b) Obtain an equation for the trajectory y (x) of the ray in the medium. (c) Determine the coordinates (x 1, y1) of the point P, where the ray intersects the upper surface of the slab-air boundary. (d) Indicate the path of the ray subsequently. [IIT 1995]

11. A quarter cylinder of radius R and refractive index 1.5 is placed on a table. A point object P is kept at a distance of mR from it. Find the value of m for which a ray from P will emerge parallel to the table as shown in the figure. [IIT 1999]

12. A light ray is incident on an irregular shaped slab of refractive index 2 at an angle of 45° with the normal on the incline face as shown in the figure. the ray finally emerges from the curved surface in the medium of the refractive index  = 1.514 and passes through point E. If the radius of curved surface is equal to 0.4 m, find the distance OE correct up to two decimal places. [IIT 2004]

www.physicsashok.in

39

OPTICS 13. A point object O is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of the convex mirror? [IIT 1976] 14. An object of height 4 cm is kept to the left of and on the axis of a converging lens of focal length 10 cm as shown in figure. A plane mirror is placed inclined at 45° to the lens axis 10 cm to the right of the lens (see figure). Find the position and size of the image formed by the lens and mirror combination. trace the rays forming the image. [IIT 1972]

15. An object is placed at 20 cm left of the convex lens of focal length 10 cm. If a concave mirror of focal length 5 cm is placed at 30 cm to the right of the lens find the magnification and the nature of the final image. Draw the ray diagram and locate the position of the final image. [IIT 1974]

16. An object is approaching at thin convex lens of focal length 0.3 m with a speed of 0.01 m/s. Find the magnitudes of the rates of change of position and lateral magnification of image when the object is at a distance of 0.4 m from the lens. [IIT 2004]

3 is placed on a horizontal 2 plane mirror as shown in the figure. The space between the lens

17. A thin biconvex lens of refractive index

4 . 3 It is found that when a point object is placed 15 cm above the lens on its principle axis, the object coincides with its own image. On repeating with another liquid, the object and the image again coincide at a distance 25 cm from the lens. Calculate the refractive index of the liquid. [IIT 2001]

and the mirror is then filled with water of refractive index

18. A convex lens of focal length 15 cm and a concave mirror of focal length 30 cm are kept with their optic axes PQ and RS parallel but separated in vertical direction by 0.6 cm as shown. The distance between the lens and mirror is 30 cm. An upright object AB of height 1.2 cm is placed on the optic axis PQ of the lens at a distance of 20 cm from the lens. If A’B’ is the image after refraction from the lens and reflection from the mirror, find the distance of A’B’ from the pole of the mirror and obtain its magnification. Also locate position of A’ and B’ with respect to the optic axis RS. [IIT 2000]

www.physicsashok.in

40

OPTICS 3 and 2 of focal length 0.3 m in air is sealed into an opening at one

19. A thin equiconvex lens of glass of refractive index  

4  end of a tank filled with water     . On the opposite side 3  of the lens, a mirror is placed inside the tank on the tank wall perpendicular to the lens axis, as shown in figure. The separation between the lens and the mirror is 0.8 m. A small object is placed outside the tank in front of the lens at a distance of 0.9 m from the lens along its axis. Find the position (relative to the lens) of the image of the object formed by the system. [IIT 1997, May]

20. A thin plano-convex lens of focal length  is split in to two halves: one of the halves is shifted along the optical axis (see figure). The separation between object and image planes is 1.8 m. The magnification of the image formed by one of the half-lenses is 2. Find the focal-length of the lens and separation between the two halves. Draw the ray diagram for image formation. [IIT 1996] 21. A plano convex lens has a thickness of 4 cm. When placed on a horizontal table with the curved surface in contact with it, the apparent depth of the bottom most point of the lens is found to be 3 cm. If the lens is inverted such that the plane face is in contact with the table, the apparent depth of the centre of the plane face is found to be 25/8 cm. Find the focal length of the lens. [IIT 1984] 22. The convex surface of a thin concavo-convex lens of glass of refractive index 1.5 has a radius of curvature 20 cm. The concave surface has a radius of curvature 60 cm. The convex side is silvered and placed on a horizontal surface. (a) Where should a pin be placed on the optic axis such that its image is formed at the same place? 4 (b) If the concave part is filled with water of refractive index , 3 find the distance through which the pin should be moved so that the image of the pin again coincide with the pin. [IIT 1981]

23. Find the focal length of the lens shown in the figure. The radii of curvature of both the surfaces are equal to R. [IIT 2003]

24. The refractive indices of the crown glass for blue and red lights are 1.51 and 1.49 respectively and those of the flint glass are 1.77 and 1.73 respectively. An isosceles prism of angle 6° is made of crown glass. A beam of white light is incident at a small angle of this prism. The other flint glass isosceles prism is combined with the crown glass prism such that there is no deviation of the incident light. Determine the angle of the flint glass prism. Calculate the net dispersion of the combined system. [IIT 2001]

25. A prism of refracting angle 30° is coated with a thin film of transparent material of  is refractive index 2.2 on face AC of the prism. A light of wavelength 5500 A incident on face AB such that angle of incidence is 60°, find (a) the angle of emergence, [Given refractive index of the material of the prism is

3 ].

www.physicsashok.in

41

OPTICS (b) the minimum value of thickness of the coated film on the face AC for which the light emerging from the face has maximum intensity. [IIT 2003] 26. A right angle prism (45° – 90° – 45°) of refractive index n has a plate of refractive index n1 (n1 < n) cemented to its diagonal face. The assembly is in air. A ray is incident on AB (see figure), (a) Calculate the angle of incidence at AB for which the ray strikes the diagonal face at the critical angle. (b) Assuming n = 1.352, calculate the angle of incidence at AB for which the refracted ray passes through the diagonal face undeviated. [IIT 1996] 27. A right angled prism is to be made by selecting a proper material and the angles A and B (B  A), as shown in figure. It is desired that a ray of light incident on the face AB emerges parallel to the incident direction after two internal reflections. (a) What should be the minimum refractive index n for this to be possible? (b)

5 is it possible to achieve this with the angle B 3 equal to 30 degrees ? [IIT 1987]

For n =

28. Monochromatic light is incident on a plane interface AB between two media of refractive indices n1 and n2 (n2>n1) at an angle of incidence  as shown in the figure. The angle  is infinitesimally greater than the critical angle for the two media so that total internal reflection takes place. Now if a transparent slab DEFG of uniform thickness and of refractive index n3 is introduced on the interface (as shown in the figure), show that for any value of n3 all light will ultimately be reflected back again into medium II. Consider separately the cases. (i) n3 < n1 and (ii) n3 > n1. [IIT 1986] 4 ) is refracted by a spherical air bubble of 3 radius 2 mm situated in water. Assuming the light rays to be paraxial, (a) find the position of the image due to refraction at the first surface and the position of the final image. (b) draw a ray diagram showing the positions of both the images. [IIT 1988]

29. A parallel beam of light travelling in water (refractive index =

30. Light is incident at an angle  on one planar end of a transparent cylindrical rod of refractive index n. Determine the least value of n so that the light entering the rod does not emerge from the curved surface of the rod irrespective of the value of  . [IIT 1992] 31. The radius of curvature of the convex face of a plano convex lens is 12 cm and its refractive index is 1.5. (i) Find the focal length of this lens. (ii) The plane surface of the lens is now silvered. At what distance from the lens will parallel rays incident on the convex face converge. (iii) Sketch the ray diagram to locate the image, when a point object is placed on the axis, 20 cm from the lens (polished). (iv) Calculate the image distance when the object is placed as in (iiii). [IIT 1979] 32. A ray of light is incident at an angle of 60° on one face of prism which has an angle of 30° with the incident ray. Show that the emergent ray is perpendicular to the face through which it emerges and calculate the refractive index of the material of the prism. [IIT 1978]

www.physicsashok.in

42

OPTICS 33. A pin is placed 10 cm in front of a convex lens of focal length 20 cm., made of a material of refractive index 1.5. The surface of the lens farther away from the pin is silvered and has a radius of curvature are 22 cm. Determine the position of the final image. Is the image real as virtual? [IIT 1978] 34. The refractive index of the material of a prism of refracting angle 45° is 1.6 for a certain monochromatic ray. What should be minimum angle of incidence of this ray on the prism so that no total internal reflection takes place as the ray comes out of the prism. [IIT 1976] 35. A prism of refractive index n1 and another prism of refractive index n2 are stuck together without a gap as shown in the figure. The angles of the prisms are as shown n1 and n2 depend on  , the wavelength of light, according to n1  1.20 

10.8  10 4 2

and

n2  1.45 

1.80  10 4 2

where,  is in nm. (a) Calculate the wavelength  0 for which rays incident at any angle on the interface BC pass through without bending at that interface. (b) For light of wavelength  0, find the angle of incidence i on the face AC such that the deviation produced by the combination of prisms is minimum. [IIT 1998] 36. A projector lens has a focal length 10 cm. It throws an image of a 2 cm x 1 cm slide on a screen 5 metre from the lens. Find : (a) the size of the picture on the screen and (b) ratio of illuminations of the slide and of the picture on the screen. [IIT 1975] 37. A ray of light incident normally on one of the faces of a right angled isosceles prism is found to be totally reflected as shown in the figure. What is the minimum value of the refractive index of the material of the prism? When the prism is immersed in water, trace the path of the emergent rays for the same incident ray, indicating the values 4  of all the angles.      . 3 

[IIT 1973]

www.physicsashok.in

43

OPTICS

Answer Key Assertion & Reasion

Assertion & Reasion Que.

1

2

3

4

5

6

7

8

9

10

Ans.

A

A

A

A

B

E

C

A

C

A

Que.

11

12

13

14

15

16

Ans.

B

D

D

B

B

D

Level # 1

Objective Type Que.

1

2

3

4

5

6

7

8

9

10

Ans.

B

C

A

A

C

C

B

D

D

C

Que.

11

12

13

14

15

16

17

18

19

20

Ans.

D

A

B

C

A

D

B

CD

C

C

Que.

21

22

23

24

25

26

27

28

29

30

Ans.

B

B

B

A

D

C

A

A

A

B

Que.

31

32

33

34

35

36

37

38

39

40

Ans.

C

C

C

A

D

A

A

C

D

C

Que.

41

42

43

44

45

46

47

48

49

50

Ans.

A

D

B

D

C

C

B

B

B

C

Que.

51

52

53

54

55

56

57

58

59

60

Ans.

B

C

A

A

B

A

BD

D

A

C

Que.

61

62

63

64

Ans.

C

BC

CD

D

Fill in the Blanks / True–False / Match Table 1. 2 x 108 m/s, 0.4 x 10–6 m

2. d = +15 cm

5. 60 cm

6.

9. Zero 15°

10. 5 x 1014 Hz, 4000Å

25 9

3. 4000Å, 5 x 1014 Hz

4. 2

7. 35 cm

8. 1.3

11. 0.125 m, 0.5 m

1 2 .

Que.

13

14

15

16

17

18

19

20

Ans.

T

F

T

T

D

A

C

B

www.physicsashok.in

44

OPTICS

Passage Type Que.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Ans.

D

B

B

C

D

B

D

D

B

A

A

C

C

A

A

Que.

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Ans.

A

B

A

B

C

A

D

B

B

A

D

D

B

B

B

Que.

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

Ans.

C

C

B

D

B

A

B

C

C

C

B

B

A

A

B

Que.

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Ans.

C

D

D

B

C

A

B

C

B

A

B

C

A

A

B

Que.

61

62

63

64

65

66

67

68

69

70

71

Ans.

D

D

C

A

B

C

C

A

D

C

D

Level # 2. 2. 1.6

7.

3. 90 cm., Yes.

4. 2.88 m

2  1   2   d   2  1   x  r 0 0 (a) A  r     (c) Ray will become parallel to y-axis.

8. –2 Km.

9. R  12 cm .

1  1 12.   i  A  sin  2

10. 7.42 cm

    sin 2 i  cos A sin i sin A 1  

A

(b)

5. (a) 13.3 cm (b) 14.975 cm 0  1 2 2  d    2 2  0     0  1   r   

  cos i t 1  x  1 11.   12  sin 2  

13.

   cos i  1   sin i  t  2   2 2  i   sin i  

a a  15   , 8 8 

 b2 b2  1  b 2    2 sin    1  14. 15. The first spot is at 12 cm on left side from the optical R  R R2    centre.   2 cos   1   , 0 16. –20 cm 17.     19. b = 15 cm.  cos   1    20. At a distance of 15 cm. from the mirror 2 cm. from each other.

21. First Image at a distance of 3.33 cm from flat surface and the second at infinity. 22. 9 cm     1 2     R 1  d  2 2  23.   2   2 25. 81°40’ 26. b b    2  2  1  2   R R  27. 25 cm from the second lens on the right side magnification m = –2. 28. 0.5 cm 29. 6 cm back side of unpolished lens.

30.  

www.physicsashok.in

7 3

45

OPTICS

Level # 3 3 ˆi  4 ˆj  5 kˆ

1. –7.67 cm from the mirror.

2.

5. 18.84 cm

6.  = sin–1 0.6115 = 38° No ray is refracted into glass.

7. 2 x 1010 cm per second.

8. 720 m x 720 m

9. (a) 14.16 cm below the water surface. 10. (a) Slop

dy  cot i dx

2 x  (b) y  K    4

3. 25 cm

5 2

4.

2

(b) No glass water interface. 4

(c) (4m, 1m)

(d) Ray emerges parallel to the positive x-axis.

4 12. OE = 6.06 m 13. 25 cm. 3 14. At a perpendicular distance of 20 cms from the lens axis 8 cm is size oriented parallel to lens axis.

11. m 

15. At the position of the object magnification = –1.

16. 0.09 m/s, 0.3 per second.

17. 1.6

18. Distance of A’B’ from pole of mirror a15 cm, magnification = –1.5. Distance of A’ above RS is 0.3 cm, Distance of B’ below RS is 1.5 cm. 19. 0.9 m from the lens (0.1 m behind the mirror)

20. (a)  = 0.4 m, d = 0.6 m.

21. 75 cm

22. (a) 15 cm

(b) 1.15 cm towards the lens

3 R 23.    3 1

24. 4°, 0.04°

25. (a) 0

(b) 1250Å

1 27. (a) sin B

(b) No.

1  1  2 2   n  n1  n1  26. (a) sin    2 

1 (b) sin

1.352

 73

2

29. (a) Image due to first surface at a distance of 6 mm before the first surface final image at a distance of 1mm before the first surface. 30.

2

31. (a) 24 cm

33. 17 cm infront of lens, Real. 36. (a) 100 cm x 50 cm

(b) 12 cm

(d) 80 cm.

34. sin 1 0.176   10.1

 slide  2401 (b)  picture

32.   3 . 35. (a)  0  600 nm

(b) i  sin1 ¾

37.   2 , Angle of refraction in water r = sin 1 ¾ .

—X—X—X—X—

www.physicsashok.in

46