A thin prism of refracting angle \(6^\circ\) is kept in air. It produces a minimum deviation of \(3.6^\circ\). The refractive index of the material of the prism is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1.6
For a thin prism the minimum deviation is small. It depends only on the angle of the prism and its refractive index, \( D_m=(n-1)A \).
\( A=6^\circ \)
\( D_m=3.6^\circ \)
\( \begin{aligned} D_m &= (n-1)A \\ 3.6^\circ &= (n-1)\times6^\circ \\ n-1 &= 0.6 \end{aligned} \)
\( n=1.6 \)
Hence, the refractive index of the material of the prism is 1.6.
NCERT (2026-27):
Refraction Through a Prism – “For a small angle prism, i.e., a thin prism, Dm is also very small, and we get”
\( \displaystyle n_{21}=\frac{\sin[(A+D_m)/2]}{\sin[A/2]}\simeq\frac{(A+D_m)/2}{A/2} \)
\( \displaystyle D_m=(n_{21}-1)A \)