A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to \( \left(\displaystyle\frac{3}{4}\right) \)th of the angle of prism. The angle of deviation is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 30^\circ \)
For a ray passing through a prism, the angles at the two faces are related by \( r_1 + r_2 = A \), which gives the angle of deviation
\( \displaystyle \delta = i + e - A \)
An equilateral prism has \( A = 60^\circ \). Here \( i = e \), which is the condition of minimum deviation.
\( \displaystyle i = e = \frac{3}{4} \times 60^\circ = 45^\circ \)
\( \displaystyle \delta = 45^\circ + 45^\circ - 60^\circ = 30^\circ \)