# Find the sin of the angle of incidence of a ray on the surface of water from air if the angle of refraction

July 28, 2021 | education

| **Find the sin of the angle of incidence of a ray on the surface of water from air if the angle of refraction of the ray in water is 30 degrees.**

From Snell’s law, the angle of incidence of light on any surface is related to the angle of refraction by the ratio:

n1 * sinα = n2 * sinβ, where

sinα / sinβ = n2 / n1, where n2 / n1 = n21 is the relative refractive index of the two media (for water, the refractive index is n21 = 1.333), β = 30º.

Let us calculate the sin of the angle of incidence of the light beam:

sinα = n21 * sinβ = 1.333 * sin30º = 1.333 * 0.5 = 0.6665 (α ≈ 42º, sin42º)

Answer: The sin of the angle of incidence of the light beam is 0.6665.

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