normal line

Meaning: The normal line is an imaginary line perpendicular (90°) to a surface at the point where a ray strikes it. All angles in ray optics are measured from it. On a curved mirror or lens surface, it is perpendicular to the tangent at that point, so on a sphere it lies along the radius. A ray along the normal has an angle of 0°, so it reflects straight back or passes straight through without bending.

Equation: θi = θr and n₁ sin θ₁ = n₂ sin θ₂. Here θ is the angle between the ray and the normal (rad, or degrees), and n is the index of refraction (dimensionless, n = c/v, with c in m/s and v the speed of light in the medium in m/s).

On the MCAT: Passages show a ray at a boundary and ask which way it bends. Entering a medium with higher n, the ray bends toward the normal; entering one with lower n, it bends away. Total internal reflection occurs beyond the critical angle, sin θc = n₂/n₁ (with n₁ > n₂), also measured from the normal. Draw the normal first when the surface is tilted or curved.

Common confusion: Students measure the angle from the surface. Both the law of reflection and Snell's law use the angle from the normal, so if a problem gives the angle to the surface, subtract it from 90° first.