Question

A ray of light passes through an equilateral prism such that an angle of incidence is equal to the angle of emergence and the latter is equal to $ \frac{3}{4} $ th the angle of prism. The angle of deviation is:

• A. $ 45{}^\circ $
• B. $ 39{}^\circ $
• C. $ 20{}^\circ $
• D. $ 30{}^\circ $
• E. $ 90{}^\circ $

Answer 1

Answer: (D)

Angle of incidence = angle of emergence, i.e., $ i = i' $
Also, $ i' = \frac{3}{4}\times $ angle of equilateral prism $ =\frac{3}{4}\times 60{}^\circ =45{}^\circ $
Thus, angle of deviation $ = i + i' - A $
$ =(45{}^\circ +45{}^\circ -60{}^\circ )=30{}^\circ $