Angle of Minimum Deviation

ANGLE OF MINIMUM DEVIATION OF PRISM Objective: Study of the variation of angle of deviation with the angle of incidence by plotting I~ D curve and hence determine the angle of minimum deviation for a given wavelength using a spectrometer. APPARATUS: Spectrometer, Prism, Sodium Lamp and Spirit level. Overview: A light ray is said to be deviated when there is a change in the path of light ray suffering reflection or refraction. When a light ray suffers from refraction, the angle between the incident ray and emergent ray is called the angle of deviation. In Fig. 1 i is the angle of incidence, r is the angle of emergence and δ is the angle of deviation. When refraction takes place, through a prism in such a manner that the angle of incidence is equal to the angle of emergence, the Fig. 1 refracted ray will be parallel to the base of the prism. The ray is symmetrical under these conditions. It can be mathematically proved that when the above conditions are satisfied for a particular value of i, the deviation suffered by the light ray is minimum and the angle of deviation is known as the angle of minimum deviation δm. For any other value of i, the value of δ increases.

Fig. 2: Experimental set up

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Procedure: 1. Become familiar with the spectrometer  Identify each component: the circular scale, the prism table, the collimator, and the telescope.  Note the clamping screws and the fine adjustment screws for the telescope. Note the clamping screw for the prism table.  Note how to adjust focusing of the slit in the collimator tube and also the telescope focus and the eyepiece.  Note how the slit width can be adjusted. 2. Determine the vernier constant (VC) of the spectrometer by filling up Table-1. 3. Practice reading the angle from the circular scale. Use the vernier scale with the little magnifying glass to read the angle to the nearest arc minute. (1 arcmin = 1' = 1/ 60 degree.) The following is an example: In the figure below, the zero point on the vernier scale is between the 155º and 155º30' (or 155.5º) marks on the degree plate. So the main scale reading (M) is 155º. Now note the vernier reading (V) by finding the line on the vernier scale that aligns most closely with any line on the main scale. From figure, V=15. Assuming the vernier constant (VC) = 1', the total reading (T) is T = 155º + (1'×15) = 155º 15' or 155.4º. For convenience convert all the readings to degrees. 4. Complete all the preliminary adjustments and focusing of the spectrometer as instructed in the supporting manual. 5. Clamp the prism table 6. Illuminate the slit of the collimator with the given source, i.e. sodium lamp. Note that the lamp takes some time to warm up before getting fully illuminated. Adjust the telescope position in line with the collimator so that the direct image of the slit is centered on the vertical crosswire. Note the reading for this position of telescope on any one of the verniers (say V1). (No need to tabulate it.) Collimator

7. Setting the angle of incidence (i): (Refer Fig. 2)  DO NOT PLACE THE PRISM ON THE SPECTROMETER YET.  Let us start with an angle of incidence, i (say 45º). To set this angle the telescope should be rotated in clockwise or anticlockwise direction from the direct image position exactly by an angle = 180-2i, i.e. (180º – 90º) = 90º, looking at the same vernier V1.  Clamp the telescope in this position. The angle between the axes of the collimator and telescope is 2i (i.e.900). Telescope position for angle of deviation

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Telescope position for angle of incidence

Fig. 2

  

Keep the prism on the prism table oriented as shown in Fig. 2. Release the prism table and turn it slowly, till the reflected image of the slit from the refracting surface AB is visible in the field of view of the telescope. Clamp the prism table. Using the fine adjustment screw allow the image of the slit to coincide with the vertical cross-wire. The prism is now adjusted for an angle of incidence i = 45º.

8. Angle of deviation (δ): (Refer Figs. 2 and 3)  Keeping the prism table clamped, slowly turn the telescope towards the second refracting surface AC (away from the collimator till the image of the slit is visible in the field of view of the telescope.  Clamp the telescope. Using the fine adjustment screw allow the image of the slit coincide with the vertical cross-wire. Note down the readings. Let the readings be θ1 and θ2 on the two verniers V1 and V2 respectively.  Remove the prism and rotate the telescope as shown by arrow in Fig. 3 to get the direct image of the slit coinciding with the vertical cross-wire. Let the readings be D1 and D2 on the two verniers V1 and V2 respectively.  The angle of deviation can then be calculated as δ θ ~D for V1 δ θ ~D for V2  Thus the mean angle of deviation for an angle of incidence i = 45º is determined as . Fig. 3

9. Repeat the above procedure (7 & 8) to find the angle of deviation , for various values of i starting from 45º to 80º in steps of 5º and fill up tables 2 & 3 simultaneously. 10. Plot a graph between angle of incidence i (X-axis) and the angle of deviation (Y-axis) and determine the angle of minimum deviation m. 11. Knowing the angle of prism and refracting index of the material of the prism, calculate the value of m and compare with the value determine from graph. Observations: Table 1: Determination of vernier constant (VC) of the spectrometer Value of 1 small main scale division (MSD) = ……… ……. vernier scale divisions = ….. main scale divisions Hence, 1 vernier scale division = ………… main scale division (VSD) Vernier Constant (VC) = (1 – VSD) x MSD = ………

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Table 2: For Vernier I i (0)

Deviated ray (θ1) (0)

M.S.R

V.C

V.S.R

Direct ray ( D1) (0)

Total

M.S.R

V.C

V.S.R

Angle of deviation δ θ ~D (0) Total

45 50 … …

Table 3: For Vernier II i (0)

Deviated ray (θ2) (0)

M.S.R

V.C

V.S.R

Direct ray ( D2) (0)

Total

M.S.R

V.C

V.S.R

Angle of deviation δ θ ~D (0) Total

45 50 … …

Table 4: data for i ~ i (0) Mean 1 2 0 ()

plot 45

50

…

…

…

…

…

…

Calculations: From graph, angle of minimum deviation,

m

= ……………

From calculation: Given, angle of prism A= 600, refractive index of the material of prism µ = 1.52 (for crown glass) and 1.62 (for flint glass)

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Using the equation,

, calculate

m

= …………

Discussions: Precautions: 1. Leveling of both the spectrometer and the prism table has to be done accurately and Prism table should be fixed to its axis. 2. The slit should be as narrow as possible. 3. Gently turn the fine adjustment screws and avoid backlash errors. 4. Carefully handle the prism. Do not touch the refracting surfaces by hand. Place the prism on the prism table or remove it from the prism table by holding it with fingers at the top and bottom faces. Reference: 1. Practical Physics, R.K. Shukla and A. Srivastava.

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