critical angle
Summary
The critical angle is the angle of incidence, in the medium with the higher index of refraction, at which the refracted ray travels along the boundary (refraction angle 90°). At larger incident angles, light undergoes total internal reflection. It exists when light goes from higher n to lower n.
Detail
Meaning: When light passes from a medium of higher index of refraction (n₁) into one of lower index (n₂), it bends away from the normal. As the angle of incidence increases, the refracted angle grows until it reaches 90° and the refracted ray skims along the boundary. The incident angle that does this is the critical angle. At larger incident angles Snell's law has no solution, and the light is completely reflected back into the first medium. This is total internal reflection.
Equation: n₁ sin θc = n₂ sin 90°, so sin θc = n₂/n₁ and θc = sin⁻¹(n₂/n₁). Here θc is the critical angle (radians or degrees, measured from the normal), and n₁ and n₂ are indices of refraction (dimensionless), with n₁ > n₂.
On the MCAT: Typical settings are fiber optics (core with higher n than cladding), prisms, and light going from water or glass into air. You may be asked whether a ray with a given incident angle will be totally reflected (yes if the angle exceeds θc), or how θc changes when n₂/n₁ gets smaller (θc decreases).
Common confusion: Angles are measured from the normal, not from the surface. The critical angle does not exist for light going from lower n to higher n, because n₂/n₁ would exceed 1 and sin θ cannot. Total internal reflection occurs at angles greater than θc; at exactly θc the refracted ray grazes the surface.
Sources
- Physics (Cutnell and Johnson)
- University Physics (Young and Freedman)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.