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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