Question

1) prove R=2f Physics question class 10​

Answer 1

Explanation:

radius of curvature =2(focal length)

if f=3cm then find r

r= 2f

r= 2(3)

r=6

Answer 2

Answer:

Consider a Concave mirror as shown in the figure above.

A ray of light SA traveling parallel to the principal axis PC is incident on a convex mirror at A. After reflection, it goes through the focus F. P is the pole of the mirror. C is the centre of curvature.

The distance PF= focal length f.

The distance PC= radius of curvature R of the mirror. 

AC is the normal to the mirror at the point of incidence B.

Angle SAC=Angle CAF (Law of reflection, angle i= angle r)

Angle SAC=Angle ACF (alternate angles) 

Hence, Angle ACF= Angle CAF

Also, ΔFAC is an isosceles triangle.

Hence, sides AF=FC

For a small aperture of the mirror, the point B is very close to the point P, So we can say, AF=PF

PF=FC=1/2 PC

which proves that f=1/2 R; Radius of curvature = 2f