Rarer medium, reflection and lenses

When the second medium is rarer (v₂ > v₁), the same construction works, but the wavelet from A now outruns point B. The refracted ray bends away from the normal (r > i), and n₁ sin i = n₂ sin r still holds.

As i grows, r reaches 90° first. The angle of incidence at which r = 90° is the critical angle ic, given by sin ic = n₂/n₁.

For any angle of incidence larger than ic there is no refracted wave at all; the light undergoes total internal reflection.

Reflection: a plane wavefront AB meets a mirror MN at angle i. While B travels BC = vτ to the mirror, the wavelet from A grows to radius AE = vτ in the same medium. The tangent CE from C is the reflected wavefront.

Triangles EAC and BAC are congruent: they share AC, have AE = BC and each has a right angle (at E and at B). Hence the angle of reflection equals the angle of incidence, which is the law of reflection.

Thin prism: the lower part of a plane wavefront crosses the most glass and is held back the most, so the wavefront comes out tilted and the beam turns.

Convex lens: the middle of the wavefront passes through the thickest glass and is delayed most. The emerging wavefront is dented at the centre, becomes spherical and converges to the focus F. A concave mirror likewise turns a plane wavefront into one converging to its focus; concave lenses and convex mirrors are explained the same way.

Every ray from a point on an object to its image takes the same time. Through a convex lens the central ray has the shortest path, but it spends longest in slow glass, so it arrives together with the rays near the edge.