#### Question

What is the focal length of a convex lens of focal length 30 cm in contact with a concave lens of focal length 20 cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses.

#### Solution

Focal length of the convex lens, *f*_{1} = 30 cm

Focal length of the concave lens, *f*_{2} = −20 cm

Focal length of the system of lenses = *f*

The equivalent focal length of a system of two lenses in contact is given as:

`1/f = 1/f_1 + 1/f_2`

`1/f= 1/30 - 1/20 = (2-3)/60 = -1/60`

`:. f = - 60 cm`

Hence, the focal length of the combination of lenses is 60 cm. The negative sign indicates that the system of lenses acts as a diverging lens

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Solution What is the Focal Length of a Convex Lens of Focal Length 30 Cm in Contact with a Concave Lens of Focal Length 20 Cm? is the System a Converging Or a Diverging Lens? Ignore Thickness of the Lenses. Concept: Refraction at Spherical Surfaces and by Lenses - Power of a Lens.