Relation between focal length (f) and radius of curvature (R).
According to law of reflection;
∠i = ∠r = θ (let)
∴ ∠OAF = ∠i + ∠r = θ + θ = 2θ
and ∠OAF ∠AFP = 2θ (because both are alternate angles)
Similarly, ∠OAC = ∠ACP θ(these are also alternate angles) ‘
In right angled ΔANC,
tanθ = AN/CN
If θ is very small, then
(i) tanθ ≈ θ and (ii) N and P are very close to each other and considered to be same point.
∴ θ = AN/CP = AN/R ………………. (1)
Similarly from right angled Δ ANF
tan 2θ = AN/FN
If 2θ is very small, then
(i) tan 2θ ≈ 2θ and (ii) N and P are very close to each other and considered to
be same point.
∴ 2θ = AN/FP = AN/f ………………….. (2)
From equations (1) and (2), we get
2θ = 2AN/R = AN/f
or 2/R = 1/f
