CHP 19

 

Answer Key

Chapter 19 1.  Y  Yellow ellow light of a certain wavelength is incident upon two slits separated by 22.5 m.

 A screen is placed p laced 1.20 m away from the slits. The distance to the first-order bright  line is 31.4 mm. What is the wavelength of  the light?   

xd   L

2

(3.14 10 m)(2.25 10 m)  (1.20 m)



589 nm



2.  A certain laser emits light with a wavelength

of 696 nm. The laser is directed at a double slit and a screen is placed 0.900 m from the slits. The first-order bright line appears 36.5 mm from the central bright line. What  is the distance between the slits?   

d 

xd  



8.7108 m

5.  A single-sli single-slitt diffraction diffraction experim experiment ent is set set up using light from a He-Cd laser (   442 nm).

 A screen screen is placed placed 0.980 0.980 m from the the slit and and the central bright line produced by the experiment has a width of 21.2 cm. What is the  width of the the slit? slit?  L   L

2w  2x 1    x 1

(6.96107 m)(0.900 m)

 (3.65102 m)

(4.42107 m)(0.980 m)







4.07106 m

(0.1065 m)

6.  A single-slit diffraction diffra ction experiment is set up

1.72105 m

3. Green light with a wavelength of 545 nm

is incident upon two slits separated by 18.0 m. A screen is set up to view the interference pattern produced and the first-order bright line is 26.4 mm from the central bright line. How far is the screen from the double slit?

using a slit with a width of 10.0 cm. The screen is placed 0.900 cm from the slit and the distance from the central bright band to the first dark line is 0.55 cm. What is the  wavelength of the light used?  L

x 1   w    

xd 



x 1w   L

L

x d 

L  

(2.64102 m)(1.80105 m)



 (5.45 10 m)



0.872 m



3

4



(5.5 10 m)(1.0 10 m)  (0.900 m)



611 nm

 





7

4.  A wire coat hanger and a mild solution

of soap and water can be used to create large soap bubbles. These bubbles have

160

7



 L

x 

  

n soapy water



 L



 4

w  

L

d   

 vacuum

(4.88 10 m)  4(1.4)

5





a multicolored appearance due to thin-film interference. If the index of refraction of the soapy water is 1.4 m what is the minimum thickness of the soap bubble when blue light with a wavelength of 488 nm is reflected?

Supplemental Problems Answer Key 

7.  A single-slit diffraction diffra ction experiment is performed using a He-Ne laser (   633 nm)

and the setup in the figure below. What will be the width of the central bright band?

Physics: Principles and Problems 

 C  o  p  y r  i    g h   t  ©   G l    e  n  c   o  e   /   M  c   G r   a  w H i   i   l    ,l    a  d  i    v i    s  i    o n  o f   T  h   e  M  c   G r   a  w -H i   l   l    C  o m  p  a n i    e   s   , I   n  c   .

 

Answer Key Chapter 19 continued Screen

10.  The aperture through t hrough which light enters the

human eye is called the iris. The average human iris has a diameter of 5.0 mm. What  is the physical limit of the height of an object viewed from 6.0 m away?  L

x obj  1.22 obj D 

0.018 cm



1.20102 cm

7



1.22(5.89 10 m)(6.0 m)  (5.0 10 m)



8.6104 m





3

11. Coherent light of wavelength 642 nm is 2   L L

2x 1   w 

2(6.33107 m)(1.20 m)







8.4103 m

(1.8104 m)

m    

8.  A grating spunknown ectroscope is used u sed to analyze light of anspectroscope wavelength. The slits

of the grating are 2.4 m apart and the angle between the central bright line and the first-order bright line is 15.8°. What is the wavelength of the light?    d  .   c   n    I  ,   s   e    i   n   a   p   m   o    C    l    l    i    H    w   a   r    G   c    M   e    h    T    f   o   n   o    i   s    i   v    i    d   a  ,    l    l    i    H    w   a   r    G   c    M    /   e   o   c   n   e    l    G    ©    t    h   g    i   r   y   p   o    C

sin

(2.4106 m)(sin 15.8°)



653 nm

9.  A spectr s pectrosco oscope pe uses u ses a grating gr ating with

11,500 lines/cm. At what angle will light  of wavelength 485 nm have its first-order  bright line? sin 

   d 

sin

x   

  

 

 6  1.1510

(1 m) (1.15106 lines)

33.9°

d 

2(6.42107 m)(0.550 m)

 2.1 10 m 

5

0.034 m



xd   L

xd 

 m L

(1.24102 m)(1.90105 m)



 (1)(0.450 m)



524 nm

lines/m

 

 L   m  L  

m    

 

11,500 lines 100 cm   cm 1m

sin1

L

two slits separated by 1.90 105 m. A first-order bright band appears 12.4 mm from the central bright band on a screen that is placed 0.450 m from the slits. Find the wavelength of the light.

d 



xd  

12. Light of an unknown wavelength falls on





1

incident upon a pair of slits separated by 21 m. If a screen is placed 0.550 m from the slits, how far from the central bright  band is the second-order bright band?



8.7107 m/line

7

4.85 10 m   8.7 10 m  



7

Physics: Principles and Problems 

Supplemental Problems Answer Key   

161

 

Answer Key Chapter 19 continued 13.  A thin layer of oil floats on water. When

light strikes the oil, colored bands are produced. One of the colors is blue (   490 nm). If the index of refraction of  oil is 1.45, what is the minimum thickness that could have produced this color?

on a diffraction grating, lines spaced at 0.54 m are produced on a screen 95 cm away. What is the spacing between the slits in the diffraction grating?    d 



 sin

1   2d  (m  ) 2 n oil

For the thinnest layer, d 

16.  When light of wavelength 540 nm shines

m 

0

 

d 



tan

  



tan1

sin  

x 

L

 

 4n oil

7



(4.9 10 m)   4(1.45)



84 nm



d 

14. Light of wavelength 612 nm falls on a single

slit 8.5105 m wide. The slit is 81 cm from a screen. How wide is the central bright band?



 

  

sin tan1

  x   L

540109 m

     0.54 m sin tan1  



540109 m sin (tan1 (.057))



540109 m sin 30°

 L L 2 



w 



x   L

0.95 m

2x 1   



2(6.12107 m)(0.81 m)

 8.5105 m



 1.1106 m

12 mm

15. Light of an unknown wavelength falls on

 C  o  p  y r  i    g h   t  ©   G l    e  n  c   o  e   /   M  c   G r   a  w H i   i   l    ,l    a  d  i    v i    s  i    o n  o f   T  h   e  M  c   G r   a  w -H i   l   l    C  o m  p  a n i    e   s   , I   n  c   .

a single slit 9.00105 m wide. A 14.1 mm  wide bright band b and is produced prod uced on a screen 85 cm away. What is the wavelength of the light? x   2 1   

162

2   L L  w 

2x  w  2L

1

2

5



(1.41 10 m)(9.00 10 m)  2(0.85 m)



750 nm





Supplemental Problems Answer Key 

Physics: Principles and Problems