Refraction by Prism: Practice Problem & Solution
There is a prism with refractive index equal to $\sqrt{2}$ and the refractive angle equal to $30^\circ$. One of the refractive surface of the prism is polished. A beam of monochromatic light will retrace its path if its angle of incidence over the refracting surface of the prism is (1992)
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 ray to retrace its path, it must strike the silvered surface normally, so $r_2 = 0$. From $r_1 + r_2 = A$, we have $r_1 = 30^\circ$. Using Snell's law at the first surface, $1 \cdot \sin(i) = \mu \sin(r_1) = \sqrt{2} \sin(30^\circ) = \sqrt{2}(1/2) = 1/\sqrt{2}$. Therefore, the angle of incidence is $i = 45^\circ$.
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