Question

the two velocities of light in two different media are 2*10⁸ m/s and 2.5*10⁸ m/s respectively. the critical angle for these media is​

Answer 1

Explanation:

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Answer 2

Answer:

The critical angle for these media is sin⁻¹ (4/5).

Concept:

Critical Angle: Critical angle is that angle of incidence for which the angle of refraction is equal to 90°.

Refractive index: Refractive index of a medium is defined as the ratio of the velocity of light in vacuum (c) to the velocity of light in that particular medium (v).

μ = c/v

where μ = Refractive index

c = Velocity of light in vacuum or air

v = Velocity of light in medium

Find:

The critical angle for the media given.

Solution:

The velocity of light in the first medium, v₁ = 2×10⁸ m/s

The velocity of light in the second medium, v₂ = 2.5×10⁸ m/s

Refractive index of the first medium, μ₁ = c/v₁

Refractive index of the second medium, μ₂ = c/v₂

Let the critical angle be a and the angle of refraction in this situation is r = 90°.

By Snell's law, we have

$\frac{\mu_2}{\mu_1} = \frac{sin \ i}{sin \ r}$

In critical angle situation, we have

i = c and r = 90°

∴ $\frac{\mu_2}{\mu_1} = \frac{sin \ a}{sin \ 90\textdegree}$

μ₂ sin 90° = μ₁ sin a

c/v₂ (1) = c/v₁ sin a                   [∵ sin 90° = 1]

1/v₂ = sin a/v₁

sin a = v₁/v₂

sin a = 2×10⁸/2.5×10⁸

sin a = 2/2.5

sin a = 20/25

sin a = 4/5

a = sin⁻¹$(\frac{4}{5} )$

Hence, the critical angle for these media, a = sin⁻¹ (4/5).

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