Reflection and Refraction — Question 8

Question 8

Minimum prism deviation determines the refractive index

A prism of apex angle A is surrounded by air. At symmetric minimum deviation, entry and exit angles are both i and the two internal angles are both r. The measured minimum deviation is D. Take A=60 degrees and D=40 degrees.

1. Derive an expression for the prism index from A and D.

2. Calculate the index and the internal and external angles.

Question 8 - Solution

Minimum prism deviation determines the refractive index

(a) Method and calculation

$$2r=A,\quad D=2i-A\Rightarrow r=A/2,\ i=(A+D)/2.$$$$\sin i=n\sin r\Rightarrow\boxed{n=\frac{\sin[(A+D)/2]}{\sin(A/2)}}.$$

(b) Interpretation and further calculation

$$\boxed{r=30^\circ,\quad i=50^\circ}.$$$$\boxed{n=\sin50^\circ/\sin30^\circ=1.53209}.$$

Physical check

The symmetric minimum-deviation condition is supplied; arbitrary prism orientations do not have equal internal angles.