to investigate the dependence of angle of deviation on the angle of incidence using a hollow prism

The minimum value of angle of deviation is called angle of minimum deviation. It is represented by the symbol Dm.

For same angle of deviation (D) there are two values of angle of incidence. One value equals ‘i’ and other value equals ‘e’. As angle ‘i’ is increased from a small value, ‘e’ decreases from large value and angle of deviation decreases. When angle of deviation is minimum (Dm), then, ‘i’ and ‘e’ becomes equal.

PROCEDURE:

1.A white sheet of paper was fixed on the drawing board with the help of drawing pins.
2.A straight line XX’ parallel to the length of the paper was drawn nearly in the middle of the paper.
3.Points Q1,Q2,Q3 and Q4 were marked on the straight line XX’ at suitable distances of about 6cm.
4.Normal’s N1Q1,N2Q2,N3Q3 and N4Q4 were drawn on points Q1,Q2,Q3 and Q4.

5.Straight lines R1Q1,R2Q2,R3Q3 and R4Q4 were drawn making angles of 400,450,500 and 550 respectively with the normals.
6.One corner of the prism was marked as A and it was taken as the edge of the prism for all the observations.
7.Prism with its refracting face AB was put in the line XX’ and point Q1 was put in the middle of AB.
8.The boundary of the prism was marked.
9.Two pins P1 and P2 were fixed vertically on the line R1Q1 and the distance between the pins were about 2cm.
10. The images of points P1 and P2 were looked through face AC.
11. Left eye was closed and right eye was opened and was brought in line with the two images.
12. Two pins P3 and P4 were fixed vertically at about 2cm apart such that the open right eye sees pins P4 and P3 as images of P2 and P1 in one straight line.
13. Pins P1,P2,P3 and P4 were removed and their pricks on the paper were encircled.
14. Steps 7 to 13 were again repeated with points Q2,Q3 and Q4 for i=450,500 and 550.
15. Straight lines through points P4 and P3 were drawn to obtain emergent rays S1T1, S2T2, S3T3 and S4T4.

16. T1S1,T2S2 ,T3S3 and T4S4 were produced inward in the boundary of the prism to meet produced incident rays R1Q1, R2Q2,R3Q3 and R4Q4 at points F1,F2,F3 and F4.
17. Angles K1F1S1,K2F2S2,K3F3S3 and K4F4S4 were measured. These angles give angle of deviation D1, D2,D3 and D4.
18. Values of these angles were written on the paper.
19. Angle BAC was measured in the boundary of the prism. This gives angle A.
20. Observations were recorded.

Following graph shows the conclusion of result-

The angle of minimum deviation for –
Water Dm = 230 C
Kerosene oil Dm = 330 C
Turpentine oil Dm = 320 C
 The refractive indices of the-
Water n = 1.32
Kerosene oil n = 1.46
Turpentine oil n = 1.44

The variation of angle of deviation with an arbitrary angle of incidence can be encapsulated into a single equation

where  is the angle of deviation at an arbitrary angle of incidence , and  is the refractive index of the prism.
Regards.