A light ray in air (n = 1.00) strikes a flat surface of a transparent material at an angle of incidence of 50°. The angle of refraction in the material is 30°. What is the refractive index of the material? (Use sin 50° = 0.766 and sin 30° = 0.500)
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Correct answer
C. 1.53
Principle or equation
Snell's law: n1 sin θ1 = n2 sin θ2.
Why this answer is correct
Let n1 = 1.00, θ1 = 50°, θ2 = 30°. Then n2 = n1 sin θ1 / sin θ2 = (1.00 × 0.766) / 0.500 = 1.532, which rounds to 1.53.
Example
If a ray goes from air (n=1) into water (n=1.33) at an angle of incidence 30°, the angle of refraction is given by sin θ2 = (1 × sin 30°)/1.33 = 0.376, so θ2 ≈ 22°.
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