Question

A converging lens is kept coaxially in contact with a diverging lens-both the lenses being of equal focal lengths. What is the focal length of the combination?

Answer 1

A converging lens is kept coaxially in contact with a diverging lens-both the lenses being of equal focal lengths.

Let f is focal length of each lens.

for converging lens,

focal length = +f

power of lens, $P_1$ = +1/f

for diverging lens,

focal length = -f

power of lens , $P_2$ = -1/f

now after combination of lenses.

P = $P_1+P_2$

= 1/f - 1/f

= 0

hence, power of combination of lenses is zero.

so, focal length of combination = 1/P = 1/0 = ∞ ( infinity )

hence, combination of lens works as a plane mirror ( focal length of plane mirror is infinity)