The distance between an object and the screen is 100 cm. A lens placed between them produces an image on the screen when the lens is placed at two positions 40 cm apart. The power of the lens is nearly:

5 diopters

At first position of lens, let the distance of lens from object and screen be u and v respectively.

∴ x + y = 100         ...........(1)

∴ At second position of lens the distance of lens from object and screen shall be v and u respectively.

∴ y – x = 40           ...........(2)

Solving equation (1) and (2) we get

y = 70 cm = $\frac{70}{100}$ = m  and  x = 30 cm = $\frac{30}{100}$ = m

∴ The power of lens is, P = $\frac{1}{f}=\frac{1}{y}+\frac{1}{x}=\frac{100}{70}+\left(\frac{100}{30}\right)=\frac{100}{21} \approx$ 5 diopters