Refraction by Prism: Practice Problem & Solution
The refractive index of the material of a prism is $\sqrt{2}$ and its refracting angle is $30^\circ$. One of the refracting surfaces of the prism is made a mirror inwards. A beam of monochromatic light entering the prism from the other face will retrace its path after reflection from the mirrored surface if its angle of incidence on the prism is: (2004)
Solution Explained:
To solve this problem, we apply the core principles of Refraction by Prism. Understanding the underlying formula is key to arriving at the correct answer below:
For the beam to retrace its path, it must hit the mirrored surface normally, so $r_2 = 0$. Since $r_1 + r_2 = A$, we have $r_1 = 30^\circ$. Using Snell's law, $1 \cdot \sin(i) = \mu \sin(r_1) = \sqrt{2} \sin(30^\circ) = \sqrt{2}(1/2) = 1/\sqrt{2}$. Therefore, the angle of incidence is $i = 45^\circ$.
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