Question

The radius of spherical mirror is 10 cm. How far will be the focus from centre of curvature

Answer 1

Hi USER__________

Here is Your Answer....!!!

_____________________

Since we know that. .....

Centre of curvature = 2 focal length

thus the Curvature will be = 2 (10) cm

thus Curvature = 20 cm

Answer 2

Consider a concave mirror

A ray of light AB travelling parallel to the principal axis PC is incident on a concave mirror at B. 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.

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

∠ABC=∠CBF (Law of reflection, ∠i=∠r)

∠ABC=∠BCF (alternate angles)

⇒∠BCF=∠CBF

∴ΔFBC is an isosceles triangle.

Hence, sides BF=FC

For a small aperture of the mirror, the point B is very close to the point P,

⇒BF=PF

∴PF=FC=1/2PC

⇒f=1/2R

Now consider a Convex mirror

A ray of light AB traveling parallel to the principal axis PC is incident on a convex mirror at B. After reflection, it goes to Dand appear to be coming from the focus F.

The distance PF= focal length f.

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

Straight line NBCis the normal to the mirror at the point of incidence B.

∠ABN=∠NBD(Law of reflection, ∠i=∠r)

∠CBF=∠DBN (vertically opposite angles)

∠NBA=∠BCF(corresponding angles)

⇒∠BCF=∠CBF

∴ΔFBC is an isosceles triangle.

Hence, sides BF=FC

For a small aperture of the mirror, the point Bis very close to the point P,

⇒BF=PF

∴PF=FC=1/2PC

⇒f=1/2R

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