For a prism, the angle of deviation is \(38^\circ\) when the angle of incidence is \(40^\circ\). The same deviation is obtained again when the angle of incidence is \(58^\circ\). The angle of the prism is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(60^\circ\)
The deviation stays the same when \( i \) and \( e \) are interchanged. So the ray incident at \(40^\circ\) leaves the prism at \(58^\circ\). Then \( \delta=i+e-A \) gives the prism angle.
\( i=40^\circ \)
\( e=58^\circ \)
\( \delta=38^\circ \)
\( \begin{aligned} A &= i+e-\delta \\ &= 40^\circ+58^\circ-38^\circ \\ &= 60^\circ \end{aligned} \)
Hence, the angle of the prism is \(60^\circ\).
NCERT (2026-27):
Refraction Through a Prism – “… that is,”
\( \displaystyle \delta=i+e-A \)\( \qquad (9.35) \)
“… This, in fact, is expected from the symmetry of i and e in Eq. (9.35), i.e., δ remains the same if i and e are interchanged.”