Question

A point source S is placed midway between two concave mirrors having equal focal length F as shown. Find the value for d for which only one image is formed.

Answer 1

Given that,

A point source S is placed midway between two concave mirrors.

Focal length of each mirror = f

We know that,

If the object is placed at center of curvature then the image formed at center of curvature.

We need to calculate the value for d for which only one image is formed

Two case will be possible for this condition.

Case (I) :

If the point source S is placed midway between two concave mirrors.

The distance of source from first mirror is R.

The distance of source from second mirror is R.

We know that,

The radius of curvature is

$R=2f$

According to figure,

Both distance of source from mirror is same.

We need to calculate the value of d

Using formula for d

$d=R+R$

Put the value into the formula

$d=2f+2f$

$d=4f$

Case (II) :

If the source is placed at distance f from each mirror then the rays from the source after reflecting from one mirror will become parallel and these parallel rays after the reflection from the other mirror the objects itself.

Then, only one image is formed.

It means, if the source is placed at focus then the only one image will be formed.

We need to calculate the value of d

Using formula for d

$d=u+u'$

Where, u = distance of source from the first mirror

u'= distance of source from the second mirror

Put the value into the formula

$d=f+f$

$d=2f$

Hence, (a). The value of d is 4f.

(b). The value of d is 2f.

Answer 2

Answer:

d=2f is the correct answer