how far an object be from the pole of a concave mirror of focal length 20 cm to form an real image whose si ze is 1/5th of the size of the object. (answer – 120cm)

Given--
Focal length of concave mirror,f = – 20cm ( – ive for concave mirror)
Size of image ,I = 1/5 of size of object = 1/5 * O,
where,I = size of image
O = size of object
object distance, u = ?
image distance = v
Solution ---
Magnification,m is given as,
m = I/O = – v/u ( ratio of size of image to size of object which is equal to ratio of image distance to object distance)
1/5 = – v/u
or, v = – u/5
now applying the mirror formula,
1/f = 1/u + 1/v
– 1/20 = 1/u – 5/u
1/20 = 1/u + 5/u as image is real so v will be negative so on putting its value it becomes positive
or, u= – 120cm

Approved