Question

Two concave lenses A and B, each of focal length 8.0 cm are arranged coaxially 16 cm apart as shown in figure. An object P is placed at a distance of 4.0 cm from A. Find the position and nature of the final image formed.

Answer 1

Given: Two concave lenses with f = −8.0 cm are placed 16 cm apart.

Using the lens formula:

`1/f = 1/v - 1/u`

Applying for lens A:

`1/-8 = 1/v - 1/-4`

`1/v = 1/-8 - 1/4`

`1/v = (-1)/8 - 2/8`

`1/v = -3/8`

v = −2.67 cm

Since v = −2.67 cm and the second lens is 16 cm away, the image distance for lens B:

u' = 16 − 2.67

= 13.33 cm

Again, usingthe  lens formula:

`1/(v') - 1/13.33 = 1/-8`

`1/(v') = 1/-8 + 1/13.33`

= −0.2

Position of the final image is 5 cm to the left of lens B.

The nature of the image is virtual and upright.

So, the image forms at −5.0 cm.