The angle of minimum deviation of a prism is 30°. If the reflective angle of the prism of 60°,  what is refractive index ?  

prism এর minimum deviation (\(\delta_m\)) \(30^\circ\) এবং prism angle (A) \(60^\circ\) দেওয়া আছে। refractive index (\(\mu\)) নির্ণয় করতে হবে।

আমরা জানি,

\(\mu = \frac{\sin(\frac{A + \delta_m}{2})}{\sin(\frac{A}{2})}\)

এখানে,

A = \(60^\circ\)

\(\delta_m = 30^\circ\)

সুতরাং,

\(\mu = \frac{\sin(\frac{60^\circ + 30^\circ}{2})}{\sin(\frac{60^\circ}{2})}\)

\(\mu = \frac{\sin(\frac{90^\circ}{2})}{\sin(30^\circ)}\)

\(\mu = \frac{\sin(45^\circ)}{\sin(30^\circ)}\)

আমরা জানি,

\(\sin(45^\circ) = \frac{1}{\sqrt{2}}\)

\(\sin(30^\circ) = \frac{1}{2}\)

সুতরাং,

\(\mu = \frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}}\)

\(\mu = \frac{2}{\sqrt{2}}\)

\(\mu = \sqrt{2}\)

\(\mu \approx 1.414\)

অতএব, prism টির refractive index 1.414 🥳।