A 1 cm high object is placed at a distance of 32 cm from a concave mirror. The image is real, inverted and 1.5 cm in size. Calculate the focal length of the mirror and the position of the image.

Given that

Distance of the object placed from a concave mirror u = -32 cm

h_o = 1cm

As the image is inverted, the magnification must be negative

h_i = -1.5

h_i/h_o = -v/u

-1.5/1 = -v/(-32)

v = -48 cm

Image is 48 cm from the pole and on the same side of the object

Mirror formula 1/f = 1/u + 1/v

1/f = -1/32 – 1/48

f = -19.2 cm

The focal length of the mirror is 19.2 cm