Question

An object 15 cm high is placed 14 cm in front of a convex mirror with a focal length of ? 16 cm. What is the image height? Answer in units of cm

Answer 1

f =-16cm
do =14 cm (distance of object)
ho = 15cm (height of object) this information is not needed.
di = ? (distance of image)
M = ? (magnification of image)

First use the mirror equation 1/f = 1/do + 1/di
Solving for 1/di = 1/f - 1/do
di = (1/-16 - 1/14)^-1 = -7.466 cm (answer for part a) . The image is located behind the mirror (negative sign). This is always true for convex mirrors.

Now to find the size of the image use the magnification equation M = -di/do

M = -(-7.466)/14 = 0.533(answer for part b). The image is 1/2 the size of the object and upright (+M = virtual image)

image height =0.533*15=8cm

Answer 2

Start with 1/f = 1/p + 1/q

1/-16 = 1/14 + 1/q

q = -7.47 cm

Then h'/h = -q/p

h'/15 = -(-7.47)/14

h' = 8 cm