Describe how you would determine the focal length of a converging lens, using a plane mirror and one pin. Draw a ray diagram to illustrate your answer.

The equipments required to determine the focal length by using a plane mirror are —

1. A vertical stand
2. A plane mirror
3. A lens
4. A pin

(i) We place the lens L horizontally on a plane mirror MM'. Set the pin P in the clamp, in such a way that the tip of the pin is vertically above the centre O of the lens and is perfectly horizontal.

(ii) Set the height of the pin till it has no parallax (i.e., if the pin and its image shift together) so that its inverted image as seen, vertically above the pin.

(ii) Now we measure the distance x of the pin P from the lens and the distance y of the pin from the mirror, using a metre rule and a plumb line.

(iv) Now we calculate the average of the two distances. This gives the focal length of the lens, i.e.,

$f = \dfrac{(x + y)}{2}$