A light ray travels inside a horizontal plate of glass, striking its upper surface at an angle of incidence of 50°. This ray is totally internally reflected at the glass-air boundary. A liquid is then poured on top of the glass.
What is the largest index of refraction that the liquid could have such that the ray is still totally internally reflected? The index of refraction of glass is 1.50.

n₂ = 1.15

Explanation:

Given,

Angle of incidence,θ₁ = 50°

refractive index of the glass,n₁ = 1.50

refractive index of liquid = ?

For largest refractive index angle of refraction should be equal to 90°.

Using Snell's law

n₁ sin θ₁ =  n₂ sin θ₂

1.50 x sin 50° =  n₂ sin 90°

n₂ = 1.15

Hence, refractive index of the liquid is equal to 1.15.

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