Question

The combined focal length of two thin lens is 24 cm and the focal length of one converging lens is 8

Answer 1

Answer: f = -12 cm

Explanation: Combined lenses is an array of  simple lenses with a common axis. The combination is useful for correction of optical aberrations which cannot be corrected by simple lenses.

When two lenses are in contact and are thin, focal lengths are related as:

$\frac{1}{F} =\frac{1}{f_{1}} +\frac{1}{f_{2}}$

If there is a distance between the lenses, the focal length will be:

$\frac{1}{F} =\frac{1}{f_{1}} +\frac{1}{f_{2}} -\frac{d}{f_{1}f_{2}}$

Since the lenses in the question above are thin and in contact, the focal length of one of them will be:

$\frac{1}{F} =\frac{1}{f_{1}} +\frac{1}{f_{2}}$

$\frac{1}{f_{2}} =\frac{1}{f_{1}} -\frac{1}{F}$

$\frac{1}{f_{2}} =\frac{1}{8} -\frac{1}{24}$

$\frac{1}{f_{2}} =\frac{-2}{24}$

$f_{2}=$ -12

The focal length of the other lens is -12 cm, with the negative sign meaning it's a converging lens.