Question

In the displacement method, a convex lens is placed in between an object anda screen. if the magnifications in the two positions are m1 and m2 and the displacement of the lens between the two positions is x , then the focal length of the lens is?

Answer 1

Given :
m1=v/u
m2=u/v
m1-m2=v/u-u/v
=v²-u²/uv
=(v+u) (v-u)/uv-------------(1)
now v-u=x
1/f=1/u+1/v
=v+u/uv
1/f=v+u/uv
from equation1 we get :
m1-m2=x/f
f=x/m1-m2
∴focal length is x/m1-m2

Answer 2

Given :

m1=v/u

m2=u/v

m1-m2=v/u-u/v

=v²-u²/uv

=(v+u) (v-u)/uv-------------(1)

now v-u=x

1/f=1/u+1/v

=v+u/uv

1/f=v+u/uv

from equation1 we get :

m1-m2=x/f

f=x/m1-m2

∴focal length is x/m1-m2