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 = `-8/3`

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 + 8/3)`

= `-56/3`

= −18.67 cm

Again, using the lens formula:

`1/(v') - 1/(-56/3) = -1/8`

`1/(v') = -1/8 - 3/56`

`1/(v') = -10/56`

v' = `-56/10`

v' = −5.6 cm

Position of the final image is 5.6 cm to the left of lens B.

The nature of the image is virtual and erect.