Question

An object 9.0 cm tall is 45 cm in front of a convex mirror with a radius of curvature of 45 cm.

A) Where is the image? distance

B) How big is it?

C) Construct a ray diagram to scale. Indicate the parallel, focal, and central rays in your diagram

Answer 1

given that ::

object distance, d₀ = 45 cm

height of the object, h₀ = 9 cm

radius of curvature, R = 45 cm

(A) using a mirror formula :

1 / d_i + 1 / d₀ = 1 / f                                     { eq. 1 }

1 / d_i = 2 / R - 1 / d₀                                                             (since, f = R/2 & f is -ve in convex mirror)

inserting the values in above eq.

1 / d_i = 2 / (- 45 cm) - 1 / (45 cm)

1 / d_i = - 3 / 45 cm

d_i = - 15 cm

image is located at behind the mirror.

magnification, m = - d_i / d₀                          { eq. 2 }

inserting the values in eq.2.

m = - (-15 cm / 45 cm) = + 1/3 cm

Image is virtual and +1/3 as large as the object.

(B) magnification, m is given as : + 1/3

h_i / h₀ = 1 / 3

h_i = (1 / 3) x (9 cm) = 3 cm

(C) a ray diagram is shown below ::