Question

A converging lens (f1 = 12.1 cm) is located 32.4 cm to the left of a diverging lens (f2 = -5.4 cm). A postage stamp is placed 34.5 cm to the left of the converging lens. Locate the final image of the stamp relative to the diverging lens.

Answer 1

The final image of the stamp relative to the diverging lens is 7.01 cm to the left side of the diverging lens.

Step-by-step explanation:

Given that,

Focal length of converging lens = 12.1 cm

Focal length of diverging lens = -5.4 cm

Object distance = 34.5 cm

We need to calculate the image distance for converging lens

Using lens formula

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

Put the value into the formula

`(1)/(v)=(1)/(12.1)-(1)/(-34.5)`

`(1)/(v)=(932)/(8349)`

`v=8.9\ cm`

We need to calculate the image distance for diverging lens

Object distance is

`u=32.4-8.9=23.5\ cm`

Using lens formula

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

Put the value into the formula

`(1)/(v)=(1)/(-5.4)-(1)/(-23.5)`

`(1)/(v)=-(181)/(1269)`

`v=-7.01\ cm`

Hence, The final image of the stamp relative to the diverging lens is 7.01 cm to the left side of the diverging lens.