Question 10
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.
Focal length of the convex lens, f1 = 30 cm
Focal length of the concave lens, f2 = −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 / f1 + 1 / f2
1 / f = 1 / 30 - 1 / 20 = 2 - 3 / 60 = - 1 / 60
So 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.
