Question

A beam of polychromatic light passes through a thin prism of prism angle \(6^\circ\). The refractive index of the material of the prism varies with wavelength \((\lambda)\) as \(n(\lambda) = a\lambda + \frac{b}{\lambda^2}\), where \(a = 3\,\mu\text{m}^{-1}\) and \(b = 0.096\,\mu\text{m}^2\). If \(\lambda_{\min}\) is the wavelength at which the angle of minimum deviation \(D_m\) is smallest, then the correct value of \(D_m\) at \(\lambda_{\min}\) is:

• A. $6.4^\circ$
• B. $4.8^\circ$
• C. $3.2^\circ$
• D. $2.4^\circ$

Hint:

For a thin prism, deviation is directly proportional to $(n-1)$. Minimizing deviation is mathematically identical to minimizing the refractive index of the material.

Answer 1

The Correct Option is B