Question

A ray R1 is incident of the plane surface of the glass slab (kept in air) of refractive index √2 at angle of incidence equal to the critical angle for this air glass system.the refractive ray R2 undergoes partial reflection and refraction at the other surface.find the angle between reflected ray R3 and the refracted ray R4 at the surface?

Answer 1

Answer on Question#52557 - Physics - Optics

A ray $R_{1}$ is incident of the plane surface of the glass slab (kept in air) of refractive index $\sqrt{2}$ at angle of incidence equal to the critical angle for this air glass system. The refractive ray $R_{2}$ undergoes partial reflection and refraction at the other surface. Find the angle between reflected ray $R_{3}$ and the refracted ray $R_{4}$ at the surface?

Solution:

Since angle of incidence $\varphi_{i}$ is equal to the critical for this air glass system, we obtain

$$\sin \varphi_ {i} = \frac {1}{n} = \frac {1}{\sqrt {2}} \Rightarrow \varphi_ {i} = \frac {\pi}{4}$$

According to the law of refraction:

$$\sin \varphi_ {i} = n \cdot \sin \varphi_ {r}$$

Therefore,

$$\sin \varphi_ {r} = \frac {\sin \varphi_ {i}}{n} = \frac {1}{2} \Rightarrow \varphi_ {r} = \frac {\pi}{6}$$

The angle $\theta$ between rays $R_{3}$ and $R_{4}$ is given by

$$\theta = \pi - (\varphi_ {i} + \varphi_ {r}) = \pi - \left(\frac {\pi}{4} + \frac {\pi}{6}\right) = \frac {7 \pi}{1 2}$$

Answer: $\frac{7\pi}{12}$

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