Question

A mirror produces an image of (+)15 cm height, when the object is placed 20 cm away from

the mirror. The object is only 10 cm in height. Calculate the focal length of the mirror.​

Answer 1

height of object, h = 10cm

height of image , hi = +15cm

magnification of mirror = height of image/height of object = 15cm/10cm= 1.5

here, height of image is larger than height of object and also magnification is greater than 1. then, mirror must be concave .

now, magnification = 1.5 = -v/u

or, 1.5 = -v/(-20cm)

or, v = +30cm

now using mirror formula,

1/v + 1/u = 1/f

or, 1/+30 + 1/-20 = 1/f

or, (20 - 30)/600 = 1/f

or, -10/600 = 1/f

or, 1/f = 1/-60 => f = -60cm

hence, focal length of mirror is 60cm