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Answer in Brief

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

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#### 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`

Concept: Spherical Mirrors

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