Snell's law, refraction and critical angle

Snell's law, refraction and critical angle

Snell's law relates the refractive indices and the sine of the angles measured from the normal: n₁ sin θ₁ = n₂ sin θ₂. Use it only after drawing the boundary and normal, because a surface angle is not an incidence angle. When light travels from a more optically dense medium to a less optically dense medium, the refracted ray bends away from the normal. At the critical angle, the refracted ray travels along the boundary; beyond it, total internal reflection occurs. Total internal reflection requires the ray to travel from higher to lower refractive index and reach an incidence angle at least as large as the critical angle.

Work it through

If light enters a material from air at 45° and refracts to 28°, n(material) ≈ sin45°/sin28° ≈ 1.51, using n(air) ≈ 1. The smaller refracted angle fits a higher refractive index because the ray bends toward the normal. A numerical answer without the normal-angle convention can still be physically wrong.

Mastery target

Use Snell's law and a ray diagram to calculate or explain refraction, critical-angle conditions and total internal reflection.