A thin plano-convex lens of focal length f is split into two halves. One of the halves is shifted along the optical axis as shown in figure. The separation between object and image planes is 1.8 m. The magnification of the image, formed by one of the ball lens is 2. Find the focal length of the lens and separation between the two halves. Draw the ray diagram for image formation.

Answer

D

Explanation

For both the halves, position of object and image is same. Only difference is of
magnification. Magnification for one of the halves is given as `2(gt1)`. Thus can be for the first
one, because for this, `|v|gt|u|`. Therefore, magnification, `|m|=|v//u|gt1`.
So, for the first half
`|v//u|=2`
`|v|=2|u|`
or Let `u=-x`,
then `v=+2x`
and `|u|+|v|=1.8m`
i.e. `3x=1.8m`
or `x=0.6m`
Hence, `u=-0.6m`
and `v=+1.2m`
using `1/f=1/v-1/u=1/1.2-1/-0.6=1/0.4`
`:. f=0.4m`
For the second half, `1/f=1/(1.2-d)-1/-(0.6+d)`
or `1/0.4=1/(1.2-d)-1/-(0.6+d)`
Solving this, we get `d=0.6m`
Magnification for the second half will be
`m_2=v/u=0.6/(-(1.2))=-1/2`
and magnification for the first half is
`m_2=v/u=1.2/-(0.6)=-2`
the ray diagram is as follows: