Question

(i) A screen is placed at a distance of 100 cm from an object. The image of the object is formed on the screen by a convex lens for two different locations of the lens separated by 20 cm. Calculate the focal length of the lens used.
(ii) A converging lens is kept coaxially in contact with a diverging lens - both the lenses being of equal focal length. What is the focal length of the combination?

Answer 1

i) Here, the distance between screen and object is $D=100cm$ and the distance between two location of convex lens is $d=20cm$.

Using the formula, the focal length $f=\frac{D^2-d^2}{4D}=\frac{{100}^2-{20}^2}{4\times 100}=24cm$

ii) If $f$ be the focal length of both lenses and $F$ be the focal length of the combination, then $\frac{1}{F}=\frac{1}{f}+\frac{1}{-f}=0$

Thus, the focal length of the combination will be infinite.