Question

Calculate the angle of incidence of light ray incident on a surface of a stab of refractive index \sqrt {3} if the angle of refraction is 30°.

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Answer 1

$\large{\bf{\gray{\underline{\underline{\orange{Given:}}}}}}$

Refractive index of glass slab = √3

Angle of refraction = 30°

$\large{\bf{\gray{\underline{\underline{\green{To\:Find:}}}}}}$

We have to find angle of incidence.

$\large{\bf{\gray{\underline{\underline{\pink{Solution:}}}}}}$

We know that,

Refractive index of air = 1

We can solve this question by using snell's law

$:\implies\sf\:n_1\sin i=n_2\sin r$

$:\implies\sf\:(1)\sin i=(\sqrt{3})\sin30\degree$

$:\implies\sf\:\sin i=\sqrt{3}\times \dfrac{1}{2}$

$:\implies\sf\:i=\sin^{-1}\dfrac{\sqrt{3}}{2}$

$:\implies\boxed{\bf{\red{i=60\degree}}}$

Answer 2

Given ,

Refractive index of glass = √3

Angle of refraction = 30°

As we know that ,

Snell's law states that the ratio of sin of angle of incidence to the sin of angle of refraction is constant

$\boxed{ \sf{ \frac{ \sin(i) }{ \sin(r) } = {}^{1}n_{2}}}$

Where ,

$\sf {}^{1}n_{2}$ = Refractive index of refracting medium with respect to the incident medium

Thus ,

Sin(i) × 1 = Sin(30) × √3

Sin(i) = 1/2 × √3

Sin(i) = Sin(60)

i = 60

∴The angle of incidence is 60°