Question

When a ray of light incident to a medium of refractive index √3 such that the angle of incidence is double the angle of refraction. The angle of refraction is​

Answer 1

Given:

The refractive index of incident medium is = √3

The angle of incidence is double the angle of refraction.

To find:

The angle of refraction.

Solution:

According to the Snell's law we know that:

$\frac{sin \: i}{sin \: r} = \frac{\mu1}{\mu 2 }$

On substituting the values in the equation we get:

$\frac{sin \: 2r}{sin \: r} = \frac{ \sqrt{3} }{1}$

$\frac{2sin \: r \: cos \: r}{sin \: r} = \sqrt{3}$

$2cosr = \sqrt{3}$

$cosr = \frac{ \sqrt{3} }{2}$

r = 30°

Thus we can say that the angle of refraction is 30°.

Answer 2

Given:

When a ray of light incident to a medium of refractive index √3 such that the angle of incidence is double the angle of refraction.

To find:

Angle of refraction?

Calculation:

Applying Snell's Law:

$\therefore\mu_{1} \times \sin(i) = \mu_{2} \times \sin(r)$

$\implies \: 1 \times \sin(2r) = \sqrt{3} \times \sin(r)$

$\implies \: \sin(2r) = \sqrt{3} \times \sin(r)$

$\implies \: 2 \sin(r) \cos(r) = \sqrt{3} \sin(r)$

$\implies \: 2 \cos(r) = \sqrt{3}$

$\implies \: \cos(r) = \dfrac{ \sqrt{3} }{2}$

$\implies \: r = {30}^{ \circ}$

So, angle of refraction is 30°.