Refraction by Prism: Practice Problem & Solution
The angle of a prism is A. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index $\mu$, of the prism is: (2014)
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 ($r_2 = 0$), so $r_1 = A$. Using Snell's law at the first surface: $\sin(i) = \mu \sin(r_1)$. Substituting $i = 2A$ and $r_1 = A$, we get $\sin(2A) = \mu \sin(A)$. Since $\sin(2A) = 2\sin(A)\cos(A)$, we find $\mu = 2\cos A$.
Leave a Reply