Question

A ray of light undergoes a minimum deviation of 60° when incident on an equilateral prism made of material of refractive index √3 The angle made by the path of the ray inside the prism with the base of the prism is

Answer 1

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Answer 2

The angle made by the path of the ray inside the prism with the base of the prism is 0°.

Step- by- step explanation:

Let's consider the equilateral prism shown in the figure.

Given;

The angle of minimum deviation- 60°

The angle of prism= 60°

Refractive index- μ

To find;

The angle made by the path of the ray inside the prism with the base of the prism.

Formula:

The formula for finding refractive index is:

μ = sin {(A+Δm)÷2}÷sin (A÷2)

Here,

μ= refractive index

A= angle of prism

Δm= angle of minimum deviation

Putting the values in equation, we get:

μ = sin{( 60 + 60)÷2÷ sin(60÷2)

μ = sin60÷sin30

μ = $\sqrt{3}/2$ ÷ 1/2

so, μ = $\sqrt{3}$

Hence proved that the prism is in the position of minimum deviation.

Therefore,

$r_{1}$= $r_{2}$ = r = 30°

So, the angle made by the ray inside the prism with surface AB;

90 - $r_{1}$= 90 - 30 = 60

Since the base also makes an angle of 60° with AB, they both are parallel.

Hence, The angle made by the path of the ray inside the prism with the base of the prism is 0°.