Question

proved by cancave mirror f=r/2 ​

Answer 1

Explanation:

Let C be the centre of curvature of the mirror. Consider a ray parallel to the principal axis striking the mirror at M. Then CM will be perpendicular to the mirror at M.

Let θ be the angle of incidence, and MD be the perpendicular from M on the principal axis. Then, ∠MCP = θ and ∠MFP = 2θ.

For small θ, which is true for paraxial rays, tan θ ≈ θ, tan 2θ ≈ 2θ. Therefore, Eq. (1)

gives Now,

for small θ, the point D is very close to the point P. Therefore, FD = f and CD = R.

Equation (2) then gives f = R/2 ---------- (3)

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