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

Answer:

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

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

$\dfrac{1}{v}=\dfrac{1}{f}-\dfrac{1}{u}$

Put the value into the formula

$\dfrac{1}{v}=\dfrac{1}{12.1}-\dfrac{1}{-34.5}$

$\dfrac{1}{v}=\dfrac{932}{8349}$

$v=8.9\ cm$

We need to calculate the image distance for diverging lens

Object distance is

$u=32.4-8.9=23.5\ cm$

Using lens formula

$\dfrac{1}{v}=\dfrac{1}{f}-\dfrac{1}{u}$

Put the value into the formula

$\dfrac{1}{v}=\dfrac{1}{-5.4}-\dfrac{1}{-23.5}$

$\dfrac{1}{v}=-\dfrac{181}{1269}$

$v=-7.01\ cm$

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