Question

A ray of light travelling inside a rectangular glass block of refractive index \[\sqrt 2 \] is incident on the glass-air interface at an angle of incidence of \[45^\circ \]. The refractive index of air is one. Under these conditions the ray will
A. Emerge into the air without any deviation
B. Be reflected back into glass
C. Be absorbed
D. Emerge into the air with an angle of refraction equal to \[90^\circ \]

Answer 1

Hint:When the light ray travels from denser medium to rare medium, the path of the light gets deviated from its original path. Using Snell’s law, you can determine the angle of refraction. The angle \[45^\circ \] is a critical angle for the refraction to still occur.

Formula used:
Snell’s law, \[{n_1}\sin {\theta _1} = {n_2}\sin {\theta _2}\]
Here, \[{n_1}\] is the refractive index of the first medium, \[{\theta _1}\] is the angle of incidence, \[{n_2}\] is the refractive index of the second medium and \[{\theta _2}\] is the angle of refraction.

Complete step by step answer:
We know that when the light ray travels from denser medium to rare medium, the path of the light gets deviated from its original path depending upon the angle of incidence and refractive index of the second medium.
We can determine the angle of refraction when the light ray emerges out of the glass slab using Snell’s law.
\[{n_1}\sin {\theta _1} = {n_2}\sin {\theta _2}\]
Here, \[{n_1}\] is the refractive index of the glass block, \[{\theta _1}\] is the angle of incidence, \[{n_2}\] is the refractive index of the air and \[{\theta _2}\] is the angle of refraction.
Substituting \[{n_1} = \sqrt 2 \], \[{\theta _1} = 45^\circ \] and \[{n_2} = 1\] in the above equation, we get,
\[\sqrt 2 \sin \left( {45} \right) = \left( 1 \right)\sin {\theta _2}\]
\[ \Rightarrow 1 = \sin {\theta _2}\]
\[ \Rightarrow {\theta _2} = {\sin ^{ - 1}}\left( 1 \right)\]
\[ \therefore {\theta _2} = 90^\circ \]
Thus, the angle of emergence is \[90^\circ \]. This angle of incidence is also known as the critical angle and it is the largest angle for which the refraction can still occur.

So, the correct answer is option D.

Note: The angle of incidence and angle of refraction are the angle made by the incident ray with normal and refracted ray with normal respectively and not with the horizontal. If the second medium is also the glass of the same thickness, then the path of light will not be affected. The refraction will not occur if the incidence angle is greater than critical angle.