question_answer

A ray of monochromatic light suffers minimum deviation of\[{{38}^{\circ }}\], while passing through a prism of refracting angle\[{{60}^{\circ }}\]. Refractive index of the prism material is:                                                                          [BHU PMT-2004]

A)  2.4                                        

B)  0.8        

C)  1.3                                        

D)  1.5

Correct Answer: D

Solution :

                 For a prism of angle \[A\] and \[\delta \] being angle of minimum deviation, refractive index of the material of prism is given by                                 \[n=\frac{\sin \,\left( \frac{A+{{\delta }_{m}}}{2} \right)}{\sin \frac{A}{2}}\] Given, \[A={{60}^{\circ }},\,{{\delta }_{m}}={{30}^{\circ }},\]                                 \[n=\frac{\sin \,\left( \frac{{{60}^{\circ }}+{{38}^{\circ }}}{2} \right)}{\sin \frac{{{60}^{\circ }}}{2}}\]                                 \[=\frac{\sin \,\,{{49}^{\circ }}}{\sin \,\,{{30}^{\circ }}}\]                                 \[n=\frac{0.7547}{0.5}=1.5\]