A ray of light traveling from a rectangular glass block of refractive index 1.5 into air strikes the block at…

Analyze the question: Light travels from glass (n = 1.5) into air (n = 1.0). The angle of incidence in the glass is 30°. We need the angle of refraction in air.

Concept: Snell's law: n₁ sin i = n₂ sin r

Going from a denser medium to a less dense one, light bends away from the normal, so the angle of refraction must be larger than 30°.

Solution:

1.5 × sin 30° = 1.0 × sin r

sin r = 1.5 × 0.5 = 0.75

r = sin⁻¹(0.75) ≈ 48.6°

Check the critical angle: sin C = 1/1.5 = 0.667, so C ≈ 41.8°. Since 30° is less than 41.8°, the ray does refract out and there is no total internal reflection.

Eliminating the other options:

• B (19.5°) and C (20.0°) are smaller than 30°. They would come from using the formula upside down (sin r = 0.5/1.5 = 0.333, r ≈ 19.5°), which is the angle for light going from air into glass.
• D (45.0°) does not match sin r = 0.75.

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Exam tip: Always check the direction of travel first.

• Dense → light (glass to air): the ray bends away from the normal, so r > i.
• Light → dense (air to glass): the ray bends towards the normal, so r < i.

If your answer goes the wrong way, you have swapped n₁ and n₂. Also, always check that the angle of incidence is below the critical angle before applying Snell's law.