Reflection and Refraction

The law of reflection — the angle of incidence equals the angle of reflection, and both are measured from the normal, the line perpendicular to the surface at the point of incidence.

Why angles are measured from the normal — measuring from the surface would break down for curved surfaces, where there is no single surface direction. The normal is always well defined.

Refraction — the change in direction of a wave crossing a boundary between media, caused by a change in its speed.

What changes and what does not — the speed and the wavelength change; the frequency does not. The source is still oscillating at the same rate, so the same number of wavefronts arrive each second as leave.

Which way it bends

Entering a slower medium (optically denser, higher refractive index), the wave bends towards the normal.

Entering a faster medium, it bends away from the normal.

Example: a useful mental picture is a car driving at an angle from tarmac onto sand. The wheel that reaches the sand first slows while the other keeps going, so the car slews round towards the normal. The same reasoning gives the direction for any boundary.

Snell's law —

n₁ sinθ₁ = n₂ sinθ₂

where the angles are measured from the normal in each medium.

Example: light passing from air into glass of refractive index 1.5 at 40° to the normal. 1.0 × sin40° = 1.5 × sinθ₂, so sinθ₂ = 0.643 ÷ 1.5 = 0.4285 and θ₂ = 25.4°. The smaller angle confirms it bent towards the normal, as entering a slower medium must.

Along the normal — a wave arriving at 0° to the normal passes straight through without changing direction, because there is no sideways difference in arrival time across the wavefront. It still changes speed and wavelength.

Partial reflection — at any boundary some light is reflected and some transmitted, which is why you can see a faint reflection of yourself in a window while also seeing through it.