question_answer

An equilateral prism is made of a material of refractive index \[\frac{4}{5}D\].The angle of minimum deviation for the prism is:

A) \[90{}^\circ \]           

B) \[60{}^\circ \]    

C) \[45{}^\circ \]

D) \[30{}^\circ \]

Correct Answer: B

Solution :

Key Idea: Equilateral prism has all angles equal to \[3.2\times {{10}^{18}}\] each. Let a prism ABC be taken. For minimum angle of deviation \[1.25\times {{10}^{13}}\] the refractive index of material of prism is given by                 \[\Omega \] Since prism is an equilateral one, its angle is \[5\times {{10}^{-3}}mho\]. Given,       \[2.5\times {{10}^{-3}}mho\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\sqrt{3}=\,\frac{\sin \,\left( \frac{{{60}^{0}}+\delta m}{2} \right)}{\sin \,\frac{{{60}^{0}}}{2}}\] \[{{10}^{5}}N/{{m}^{2}}\]  \[\sqrt{200}m/s\] \[\sqrt{400}m/s\] \[\sqrt{500}m/s\] \[\sqrt{800}m/s\] Hence, minimum angle of deviation is equal to angle of prism. Note: A prism has only one angle of minimum deviation.