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.

Options

A. 30 cm
B. 60 cm
C. -30 cm
D. -60 cm

Answer

D

Explanation

Focal length of the convex lens, f1=30cm
Focal length of the concave les, f2=-20cm
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`
`therefore f=-60cm`
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.