Snell's-law and total-internal-reflection clinic

Snell's-law and total-internal-reflection clinic

A refraction problem has a repeatable order: draw a boundary and normal; label medium indices and ray direction; write angles from the normal; apply n₁ sin θ₁ = n₂ sin θ₂; then explain the physical direction of bend. For total internal reflection, explicitly check two conditions: high-to-low refractive-index travel and an incidence angle at least equal to the critical angle. In a calculation, a sine value above 1 signals that an ordinary refracted ray is impossible under that geometry and may indicate total internal reflection or an input error.

Work it through

Light travels from a material with n = 1.41 into air. If the refracted angle would be 90°, the critical angle satisfies sin c = 1/1.41 ≈ 0.709, so c ≈ 45°. At an incidence angle larger than 45° inside the material, total internal reflection occurs. Write the travel direction first; the same 45° does not cause TIR for light entering the material from air.

Mastery target

Complete a refraction or TIR problem with a labelled ray diagram, normal-angle equation, numerical calculation and a statement of physical conditions.