Question

1. a beam of light is incident at 60 to a plane surface. The reflected and refracted rays are perpendicular to each other. What is the refractive index of the surface?

Answer 1

Given,

The angle of incidence for a beam of light = 60°

The reflected and refracted rays are perpendicular to each other.

To find,

The refractive index of the surface.

Solution,

We can simply solve this numerical problem by using the following process:

As per the laws of reflection;

The angle of incidence = angle of reflection

{Equation-1}

Also, as per Snell's law;

Refractive index = Sine (angle of incidence) / Sine (angle of refraction)

{Equation-2}

Now, according to the question and using equation-1, we get;

Angle of reflection

= angle of incidence

= 60°

=> Angle between the reflected ray and the median line = 60°

Angle between the reflected ray and the median line = 60°

{Equation-3}

Now, geometrically;

(Angle between the reflected ray and the median line) + (angle between the reflected ray and the refracted ray) + (angle between the refracted ray and the median line) = 180°

{Supplementary angles}

=> 60° + 90° + (angle between the refracted ray and the median line) = 180°

{using equation-3}

=> (angle between the refracted ray and the median line) = 30°

=> angle of refraction = 30°

Now, according to the equation-2;

Refractive index

= Sine (angle of incidence) / Sine (angle of refraction)

= Sine (60°) / Sine (30°)

= (√3/2)/(1/2)

= √3 = 1.732 approx.

Hence, the refractive index of the surface is equal to √3, which is approximately equal to 1.732.