Answer key: Refraction & Total Internal Reflection Worksheet
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Goal: Use Snell’s law, n₁ sin θ₁ = n₂ sin θ₂, to predict how light bends between materials, and find the critical angle for total internal reflection.
Completed results table
| Setting | Refracted angle | Critical angle | Behavior |
|---|---|---|---|
| Air → glass at 35° | 22.48° | Not applicable | Transmission |
| Glass → air at 35° | 59.36° | 41.81° | Transmission |
| Glass → air at 60° | No transmitted ray | 41.81° | Total internal reflection |
| Glass → air at 41° | 79.77° | 41.81° | Transmission |
| Glass → air at 42° | No transmitted ray | 41.81° | Total internal reflection |
| Air → water at 35° | 25.55° | Not applicable | Transmission |
Answers
Going from air into glass, did the light bend toward or away from the normal? Why?
Toward the normal: 35° became 22.48°. Light slows down in glass (higher n), so sin θ₂ = 1 × sin 35° ÷ 1.5 is smaller and the ray bends toward the normal.
Going from glass to air at 35°, what is the refracted angle? Why is it larger than 35°?
59.36°. Light speeds up as it leaves the glass, so sin θ₂ = 1.5 × sin 35° ÷ 1 is larger than sin 35° and the ray bends away from the normal.
What happened at 60° going from glass to air? Use the critical angle to explain.
No light passed into the air: total internal reflection. The critical angle is arcsin(1 ÷ 1.5) = 41.81°, and 60° is larger, so Snell’s law would need sin θ₂ = 1.5 × sin 60° ≈ 1.3, which is impossible.
Compare 41° and 42°. What happens to the refracted ray as you approach the critical angle?
At 41° the refracted ray leaves at 79.77°, almost along the surface. At 42°, just past the 41.81° critical angle, it disappears and all the light reflects back into the glass.
Light enters water (n = 1.33) and glass (n = 1.5) at the same 35°. Which bends it more, and why?
Glass: the refracted angle is 22.48° in glass and 25.55° in water. The larger the refractive index of the second material, the more the light slows and the more it bends toward the normal.
Challenge: what is the critical angle for light going from water (n₁ = 1.33) into air? Predict, then check it in the lab.
arcsin(1 ÷ 1.33) = 48.75°. It is larger than glass’s 41.81° because water’s refractive index is closer to air’s.