Question

a point source of light is placed at the bottom of water lake if the area illuminated circle on the surface is equal to 3 times the square of the depth of the lake then the refractive index of the water is then the refractive index of the water is ​

Answer 1

The refractive index of the water is μ = √ 1 + π / 3

Explanation:

Light of the source emerges out of water only when the incident angle at the water air boundary equals critical angle. (θc)

Let depth of lake = H

Radius of Illuminated circle = R

We are given:

πR^2 = 3H^2

H^2 = π/3.R^2

Sin(θc) = R / √ R^2 + H^2

Sin(θc) = 1/√ μ

μ = √ R^2 + H^2 / R = R √1 + π / 3 / R

μ = √ 1 + π / 3

Hence the refractive index of the water is μ = √ 1 + π / 3

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A beam of light passes from air into a substance X . If the angle of incidence be 72 degree and the angle of refraction be 40 degree , calculate the refractive index of substance X ?

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