Lecture 29: Reflection and Refraction from Spherical Surfaces

Readings: Textbook pages 1161-1172

Main Laws for both Concave and Convex mirrors, as well as plane mirror

Position of the image 1/s' + 1/s = 1/f f=R/2 or 1/s' = 1/f - 1/s
Lateral magnification m = -s'/s
Sign rules: Curvature of the concave reflective surface is taken positive, R > 0, f > 0 , (outgoing rays on the same side as curvature center), but curvature of the convex reflective surface is negative, R > 0, f > 0 , (outgoing rays are on the other side)

Case of a planar mirror is also covered by the same formulae. Just put R to infinity

Position of the image 1/s + 1/s' = 0 thus s' = -s

Lateral magnification m = - s'/s = 1

Incoming ray	Outgoing ray
Ray parallel to optical axis	passes through the focus
Ray passing through the focus	becomes parallel to the optical axis
Ray passing through the center of curvature	Backtracks itself
Ray passing through the vertex of the mirror	Reflects at the same angle as incident ray

Flash Animation: a concave circular section mirror

Flash Animation: a convex circular section mirror

Position of the image n_a/s + n_b/s' = (n_b - n_a)/R
Lateral magnification m = - s'/s n_a/n_b
Sign rules are the same, but notice that convex refractive surface has outgoing rays at the same side as its curvature center. So curvature of the convex refractive surface is positive !

Case of a planar surface is also covered. Just put R to infinity

Position of the image n_a/s + n_b/s' = 0