Question

A thin convex lens (${L_1}$) of focal length 80cm and a thin concave lens (${L_2}$ ) of focal length f are kept coaxially, 20cm apart as shown in figure. When a narrow and parallel beam of light is incident on the convex lens, the beam emerging from the concave lens is also a parallel beam. Find f.

Answer 1

Hint: In a convex lens, when the light passes through it the light rays bends towards each other whereas in a concave lens when the light passes through it the light gets spread out. Moreover the curve of the convex lens is towards the inside and the curve of the concave lens is towards the outside.

Complete answer:
The term convex lens is also known as ‘Converging lens’ or positive lens. Whereas the term concave lens is also known as ‘Diverging lens’ or negative lens. For long sightedness or hypermetropia the convex lens is used and for short sightedness or myopia the concave lens is used.
According to this question:
After refraction the parallel rays through the convex lens will converge at focus. This means that the convex lens will focus at 80cm.
So, we know that
$
  \dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u} \\
  \dfrac{1}{f} = \dfrac{1}{\infty } - \dfrac{1}{{60}} \\
$
So, we get f= -60cm
The focal length of the concave lens is 60cm.
Concave lens or diverging lens, means that it spreads out light rays that have been refracted through it. A convex lens is thinner from its centre than its edges, and is used to correct short-sightedness or we can say myopia.

Note: There are some examples of convex lens i-e telescope, the human eye, microscope, etc. however there are some examples of concave lenses also i-e lights, flashlight, laser, binocular etc. A lens is a piece of transparent glass substance which is either curved from inside or either curved from outside.