Refraction by Prism: Practice Problem & Solution
The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is $30^\circ$. One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is: (2018)
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:
To retrace its path, the ray must strike the silvered surface normally, meaning $r_2 = 0$. From $r_1 + r_2 = A$, we get $r_1 = A = 30^\circ$. Applying Snell's law at the first surface: $1 \cdot \sin(i) = \mu \sin(r_1) = \sqrt{2} \sin(30^\circ) = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}$. Therefore, the angle of incidence is $i = 45^\circ$.
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