Two prism made of material of same refractive index and having angles of the prism \( 65^\circ \) and \( 60^\circ \) respectively are combined to form a glass block as shown. If for any ray passing across the block the minimum angle of deviation in \( 3^\circ \) then refractive index for the material of the prism is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1.6
For a prism of angle \( A \), the deviation is taken as \( \delta = (\mu - 1)A \) (the thin-prism relation). In the block the second prism is placed inverted, so it deviates the ray the opposite way and the two deviations subtract.
\( A_1 = 65^\circ \)
\( A_2 = 60^\circ \)
\( \displaystyle \delta = (\mu - 1)A_1 - (\mu - 1)A_2 = (\mu - 1)(A_1 - A_2) \)
\( \displaystyle 3^\circ = (\mu - 1)(65^\circ - 60^\circ) = (\mu - 1) \times 5^\circ \)
\( \mu - 1 = 0.6 \)
\( \mu = 1.6 \)