Question

Derive the relation between f and R for a spherical mirror.

Answer 1

1. C be the center of curvature of the mirror
2. F be the principal focus.
3. Line CM is normal to the mirror at M.
4. i be the angle of incidence
   ∠MCP = i and ∠MFP = 2 i

(a) Concave mirror

(b) Convex Mirror

ΔMCP, 

tan i = `"PM"/"PC"`

ΔMFB, tan 2i = `"PM"/"PF"`

i = `"PM"/"PC" and "2i" = "PM"/"PF"`

`2"PM"/"PC" = "PM"/"PF"`; 2PF = PC

∵ PF = f

PC = R

2f = R (or) f = `"R"/2`