Question

a point object ' O 'is placed between two concave mirrors placed at a distance d apart then the value of the for which object and image coincide is (each mirror has focal length f)
a) f,2f
b) 2f,3f
c) f,4f
d) 2f,4f
​

Answer 1

Explanation:

The distances will be denoted in boldface and the values to be used in the formula (by sign convention) will be in italics.

For the first reflection from mirror in the right,

u=

2

d

,u=−u,f=−F

v

1

=

f

1

−

u

1

=

F

−1

−

d

−2

v=

2F−d

dF

v=

d−2F

dF

For the mirror opposite to the first one, u

1

=d−v

u

1

=

d−2F

d

2

−3dF

We already know that v

1

=

2

d

u

1

=−u

1

,v−v

1

,f=−F

So we have

d

−2

+

3dF−d

2

d−2F

=

F

−1

Solving this we get d−2F=0 or d

2

−4dF=0

So d=2F or d=4F or d=0

But d cannot be zero (from the figure)

So d=2F or d=4F

Note that v or u can be ±∞