Question

For light incident from air onto a slab of refractive index 2, maximum possible angle of refraction is:
A.\[{90^ \circ }\]
B.\[{60^ \circ }\]
C.\[{45^ \circ }\]
D.\[{30^ \circ }\]

Answer 1

Hint: This is a case of the phenomenon of refraction of light. According to this phenomenon, when the ray of light travels from one medium to another medium, it changes its speed and bends according to the medium.

Formula Used:
Snell’s law of refraction will be used here. According to this law, for a given pair of mediums, the sine of angle of incidence to the sine of angle of refraction is equal to a constant. Mathematically, Snell’s law can be written as,
\[\dfrac{{\sin i}}{{\sin r}} = \dfrac{{{\mu _2}}}{{{\mu _1}}} = \text{constant}\]
Where ‘i’ is the angle of incidence and ‘r’ is the angle of refraction

Complete step by step solution:
The refractive index of glass is \[{\mu _2} = 2\].
It is known that the refractive index of air is \[{\mu _1} = 1\].
Using Snell’s Law, \[{\mu _1}\sin i = {\mu _2}\sin r\]……(i)
Now according to total internal reflection, the maximum angle at which light can refract is \[{90^ \circ }\] and after that reflection occurs. Therefore, according to the situation given
\[\angle i = {90^ \circ }\].

Substituting the values in equation (i) and solving, we get
\[1 \times \sin 90 = 2 \times \sin r\]
\[\Rightarrow \sin r = \dfrac{1}{2}\sin 90\]
\[\Rightarrow \sin r = \dfrac{1}{2} \times 1\]
\[\Rightarrow \sin r = \dfrac{1}{2}\]
\[\Rightarrow r = {\sin ^{ - 1}}\dfrac{1}{2}\]
\[\therefore r = {30^ \circ }\]
The maximum possible angle of refraction for light incident from air to glass slab is \[{30^ \circ }\].

Hence, Option D is the correct answer.

Note: When a ray of light passes from a rarer to denser medium, its speed decreases and it bends towards the normal. As, in this case, the ray of light is travelling from air to glass slab, the medium and hence the speed of light will decrease. On the other hand, when the ray of light travels from denser to rarer medium, its speed changes and it bends away from the normal.