Question

A convex mirror has a radius of curvature of 46.7 cm. A 11.5-cm-tall object is placed in front of the mirror and produces an image that is 5.13-cm tall.

(a) What is the magnification?

(b) How far is the object from the mirror?

Answer 1

Radius of the convex mirror = R = -47.7 cm (Negative as it is a convex mirror)

Focal length of the convex mirror = f

f = R/2

f = -47.7/2 cm

f = -23.85 cm

Height of the object = h_o = 10.2 cm

Height of the image = h_i = 5.73 cm

Magnification of the image = M

M = 0.562

Distance of the object from the mirror = d_o

Distance of the image from the mirror = d_i

By Mirror Equation,

d_o = 18.6 cm

a) Magnification of the image = 0.562

b) Distance of the object from the mirror = 18.6 cm