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Refract a light ray from a polymer into oil

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Chemical and Physical Foundations

A light ray traveling through a transparent polymer with index of refraction 1.501.50 strikes a planar boundary at an angle of 30.0∘30.0^\circ from the normal. The air on the other side of the boundary is replaced by a transparent oil with index of refraction 1.251.25. What is the angle of refraction in the oil?

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Answer: B (36.9∘36.9^\circ)

Snell's law gives n1sin⁡θ1n_1\sin\theta_1=n2sin⁡θ2{}=n_2\sin\theta_2. After the air is replaced by oil, n1=1.50n_1=1.50, θ1=30.0∘\theta_1=30.0^\circ, and n2=1.25n_2=1.25. Therefore, sin⁡θ2\sin\theta_2=(1.50)sin⁡(30.0∘)1.25{}=\frac{(1.50)\sin(30.0^\circ)}{1.25}=0.600{}=0.600, so θ2=36.9∘\theta_2=36.9^\circ.

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