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Question
Derive the relation between f and R for a spherical mirror.
Solution
- C be the center of curvature of the mirror
- F be the principal focus.
- Line CM is normal to the mirror at M.
- 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`
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