Question

The relation between focal length f and radius of curvature R of a spherical mirror is.

Answer 1

Answer:

For a concave mirror:

In figure (a),

$$∠BP'C = ∠P'CF$$ (alternate angles) and

$$∠BP'C = ∠P'F$$ (law of reflection,$$∠i=∠r$$)

Hence $$∠P'CF = ∠CP'F$$

∴ FP

′

C is isosceles.

Hence, P

′

F=FC

If the aperture of the mirror is small, the point P

′

 is very close to the point P,

then P

′

F=PF

∴ PF=FC=

2

PC

​

or f=

2

R

​

For a convex mirror:

In figure (b),

$$∠BP'N = \angle FCP'$$ (corresponding angles)

$$∠BP'N = ∠NP'R$$ (law of reflection, $$∠i=∠r$$) and

$$∠NP'R = ∠CP'F$$ (vertically opposite angles)

Hence $$∠FCP' = ∠CP'F $$

∴ FP

′

C is isosceles.

Hence, P

′

F=FC

If the aperture of the mirror is small, the point P

′

 is very close to the point P.

Then P

′

F=PF

∴PF=FC=

2

PC

​

or f=

2

R

​

Thus, for a spherical mirror {both concave and convex), the focal length is half of its radius of curvature.

Answer 2

Answer:

focal length =1/2R

or

R=2 focal length

Explanation:

The radius of curvature is defined as the radius of the sphere of which the mirror was a part.

The focal length of the mirror is the distance between the centre of curvature till the pole of the sperical mirror.

The focal length of a spherical mirror is half the radius of curvature of that spherical mirror.

Or it can also be said as the radius of curvature is twice the focal length of that spherical mirror.

Hope this helps :):):):)