Question

A ray of light incidents at an angle of incidennce 60° on a refracting surface. If the and refracted rays are perpendicular to each other, the refractive index of the medium is ?
options :-
$\bold{a) \: \sqrt{3} }$
$\bold{b) \: \frac{ \sqrt{3} }{2} }$
$\bold {c) \: 2 \sqrt{3}}$
$\bold{ d) \: \sqrt{2}}$
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Answer 1

Correct question :-

A ray of light incidents at an angle of incidennce 60° on a refracting surface. If the reflected and refracted rays are perpendicular to each other, the refractive index of the medium is ?

options :-

$\bold{a) \: \sqrt{3} }$

$\bold{b) \: \frac{ \sqrt{3} }{2} }$

$\bold {c) \: 2 \sqrt{3}}$

$\bold{ d) \: \sqrt{2}}$

Solution :

Explanation of Diagram ( refer attached picture for rough diagram ) :-

• A ray of light is made incident on a surface. Angle of incidence is 60°.

• When light is made incident on the surface some of rays are refracted but some are reflected back. Angle of reflection is equal to angle of incidence. Therefore , rays gets reflected at 60°.

• It is given in the question that reflected rays and refracted rays are perpendicular to each other. This means that angle between them is 90°.

• Dotted line is Normal which is perpendicular to the surface.

Now , let angle of refraction be x.

=> 60° + 90° + x = 180°

=> 150° + x = 180°

=> x = 180° -150°

=> x = 30°

Therefore, refracted is at 30° from normal.

Now , by using Snell's law :-

=> μ_1 sin i = μ_2 sin r

where :-

• μ_1 = refractive index of medium 1 = 1 [ because refractive index of air is taken as 1]

• sin i = Sin 60°

• Sin r = 30°

• μ_2 = refractive index of medium 2

=>1 sin 60° = μ_2 sin 30°

We know that :-

Sin60° = √3 /2

Sin 30° = 1/2

=> √3/2 = μ_2 × 1/2

=> (√3/2 )× 2= μ_2

=> √3= μ_2

Therefore , refractive index of medium = √3

Answer :

• Option (a)√3 is correct