Angle of Minimum Deviation for Prism: Plotting Graph, Angle of Incidence, Angle of Deviation

Dispersion is defined as the separation of white light into different colours when the light is passed through the prism. The amount of scattering depends on the wavelength of light. As the angle of incidence increases, the angle of deviation decreases till it reaches a minimum value and then it increases. The least value of deviation is called angle of minimum deviation is denoted by ∂. A Prism has three rectangular surfaces and two triangular faces inclined at an angle. The angle between the two refracting surfaces is called the angle of the prism. The angle between the incident ray and the emergent ray is called the angle of deviation of the prism.

Key Terms: Prism, Angle of Deviation, Dispersion, Angle Of Minimum Deviation, Angle of Incidence, Refraction, Reflection

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Aim of Experiment 

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To determine angle of minimum deviation for a given prism by plotting a graph between angle of incidence and the angle of deviation.

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Apparatus of Experiment 

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• Drawing board
• a white sheet of paper
• prism
• drawing pins
• pencil
• half-metre scale
• office pins
• graph paper
• a protractor.

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Theory of Experiment 

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The refractive index of the material of the prism is given by

where,

D_m= angle of minimum deviation and A angle of the prism.

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Ray Diagram 

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Refraction through prism at different angles.

Ray Diagram

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Procedure of Experiment 

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1. Using drawing pins or tape, fix a plain white sheet of paper on the drawing board.
2. Carefully draw a straight line XX’ in the middle of the paper parallel to the length of the paper.
3. On the XX’ line, mark points Q1,Q2,Q3,.. at suitable distances of about 5 cm.
4. Draw normals N1Q1, N2Q2, N3Q3,... on points Q1, Q2, Q3,... as shown.
5. Making angles of 35, 40,.. 60 draw straight lines R1Q1, R2Q2, R3Q3 respectively with the normals (write value of the angles on the paper).
6. Mark A as the comer of the prism and take it as the edge of the prism for all the observations.
7. Place the prism with its refraction face AB on line XX’ and Q1 in the middle of AB.
8. Carefully, mark the boundary of the prism.
9. Fix two or more than two office pins P1 and P2 vertically on the line R1Q1. The distance between the pins should either be 10 mm or more.
10. Observe the images of point P1 and P2 through face AC.
11. Close your left eye and with the right eye open, bring it in line with the two images.
12. Fix P3 and P4 office pins vertically both10 cm apart, such that the open right eye sees pins P4 and P3 and images of P2 and P1 in one straight line.
13. Carefully remove pins P3 and P4 and encircle their pricks on the paper.
14. Repeat steps 7 to 13 for Q2, Q3,... for i= 40°,..., 60°.

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Final Outcome of Experiment 

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Observations

Observations of experiment can be written in below table:

Calculation

In order to plot the graph between the angle of incident and the angle of deviation, take the angle of incident along the x-axis and the angle of deviation along the y-axis. Minimum deviation Dm can be found from the graph which would be corresponding to the lowest point in the graph.

Let the value of angle of minimum deviation, 

Then,

Result

1. Refractive index of the material of the prism, n=......
2. Angle of minimum deviation, D_m=....
3. Graph indicates that the angle of incidence(i) increases, the angle of deviation(D) first decreases, attains a minimum value(Dm) and only then starts increasing further for the angle of incidence.

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Precautions

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1. The angle of incidence should lie between 35°-60°.
2. The pins should be fixed vertical and the distance between the pins should not be less than 8cm.
3. Arrow heads should be marked to represent the incident and emergent rays.
4. The same angle of prism should be used for all the observations.

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Sources of Errors

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1. The pins are not fixed vertically.
2. Pin pricks may be thick.
3. Measurement of angles may be wrong.
4. Prism is distributed while taking observations.

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Things to Remember

• Dispersive Power is defined as the ratio of the angular dispersion for these two colours to the mean deviation produced by the prism.
• Angular deviation depends on :(i) Angle of prism (ii) refractive index.
• The angle between the emergent rays of any two colours is called angular dispersion of those two colours.
• Refractive index is smallest for red colour and that is highest for violet colour
• If the emergent ray is reversed, then angle e becomes i and angle i becomes e. The reversed ray will have the same deviation as before.
• The least value of the angle of deviation is called the angle of minimum deviation.