JEE Main & Advanced
Physics
Question Bank
Prism Theory and Dispersion of Light
question_answer
A ray of monochromatic light is incident on one refracting face of a prism of angle 75°. It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is \[\sqrt{2}\], the angle of incidence on the first face of the prism is [EAMCET 1983]
A) 30°
B) 45°
C) 60°
D) 0°
Correct Answer:
B
Solution :
From figure \[A={{r}_{1}}+c={{r}_{1}}+{{\sin }^{-1}}\left( \frac{1}{\mu } \right)\] \[\Rightarrow {{r}_{1}}=75-{{\sin }^{-1}}\left( \frac{1}{\mu } \right)\] \[\Rightarrow 75-45={{30}^{o}}\] From Snell?s law At B \[\mu =\frac{\sin i}{\sin {{r}_{1}}}\]\[\Rightarrow \sqrt{2}=\frac{\sin i}{\sin {{30}^{o}}}\]\[\Rightarrow i={{45}^{o}}\]