A convex mirror produces a virtual image that is three fifth

A convex mirror produces a virtual image that is three fifths the size of the object.

(a) Determine the image distance if the object is 35.0 cm in front of the mirror. (Indicate the direction with the sign of your answer.)
__________cm

(b) Determine the focal length of the mirror. (Indicate the direction with the sign of your answer.)
__________ cm

Solution

a) for virtual image,

m = + 3/5 and m = -di/do

- di/do = 3/5

di = -3do/5

object distance, do = 35 cm (given)

then di = -3 x 35/5 = - 21 cm

b) using lens equation,

1/f = 1/di + 1/do

1/f= 1/35 - 1/21

f = - 52.5