Question

A small statue has a height of 3.6 cm and is placed in front of a concave mirror. The image of the statue is inverted, 1.6 cm tall, and located 16 cm in from the mirror. Find the focal length of the mirror

Answer 1

A concave mirror has a real focal length +f, image distance v = 16.0cm

Finding the object distance (u) from magnification ..

M = v/u = 1.6cm / 3.6cm = 0.44
u = v/M .. 16cm / 0.44 .. .. u = 36cm

Applying .. 1/f = 1/v + 1/u

1/f = 1/36cm + 1/16cm .. .. .. 1/f = 0.090.. .. .. ?f = 11.07 cm

Answer 2

f = 11.07cm

Method:
Start with the magnification = m = hi / ho = -1.6 cm / 3.6 cm = -0.444

This is also the ratio of image/object distances:
m = -di / do; do = -di / m = -16 cm / -0.44 = 36.03 cm

Finally, use 1/f = 1/do + 1/di = 1/36.03 cm + 1/ 16cm = 0.0277 + 0.0625 = 0.514 ; f = 1 / 0.909 = 11.07 cm