Question

Two students in a physics laboratory each have a concave mirror with the same radius of curvature, 45 cm. Each student places an object in front of a mirror. The image in both mirrors is three times the size of the object. However, when the students compare notes, they find that the object distances are not the same. What is the distance of the closer object?

Answer 1

R = radius of curvature of mirror = 45 cm

f = focal length of the mirror

Focal length of the mirror is given as

f = R/2

f = 45/2 = 22.5 cm

d_i = image distance

d_o = object distance

Given that :

h_i/h_o = 3

we know that

- d_i/d_o = h_i/h_o

- d_i/d_o = 3

d_i = - 3 d_o

using mirror equation

1/d_i + 1/d_o = 1/f

1/(- 3 d_o) + 1/d_o = 1/f

1/(- 3 d_o) + 1/d_o = 1/22.5

d_o = 15 cm