Question

prove that f= r/2 for a concave mirror. Please answer urgently .

Answer 1

refer the attachment

Answer 2

Given :

A concave mirror

To Find :

Prove f = $\frac{R}{2}$

Solution :

Let MOM₁ be a concave mirror of small aperture. C, F, O be the centre of curvature, focus and pole of the mirror respectively.

∴         ∠PQC  = ∠FQC          (∵ PQ and CO are parallel)

∴           ∠PQC  = ∠QCF          ( Alternate angles)

∴           ∠FQC  = ∠QCF           ( As ΔQCF is an isosceles triangle)

Hence,       FQ =  FC

Since aperture is very small, Q and O are very close to each other.

So, FQ = FO

∴   FO = FC

⇒  FO = $\frac{1}{2}$ OC

i.e., f = $\frac{r}{2}$ , where f = Focal length and r = radius of curvature.

Hence proved, f = $\frac{r}{2}$.