Question

It is desired to create a virtual image one fourth the object's size suing a mirror with a radius of curvature that has a magnitude of 20 cm.

A) What kind of mirror (convex, concave, or flat) should be used and why? Explain your reasoning.

B) Draw the diagram showing the object, mirror, and image. Use a straightedge to carefully draw 4 principal rays to show where the image is formed.

C) Calculate the object and image distances. Explain your reasoning.

Answer 1

A)

Convex

This is because a convex mirror forms virtual , diminshed and upright image of the object.

B)

C)

h_i = image height

h_o = object height

di = image distance

do = object distance

Given that :

h_i = h_o/4

h_i /h_o = 1/4

we know that , - d_i/d_o = h_i /h_o

- d_i/d_o = 1/4

d_i = - 0.25 d_o

R = radius of curvature = 20 cm

f = focal length = - R/2 = - 20/2 = - 10 cm

using the mirror equation

1/f = 1/d_i + 1/d_o

- 1/10 = 1/(- 0.25 d_o ) + 1/d_o

d_o = 30 cm

and

d_i = - 0.25 d_o = - 0.25 x 30 = - 7.5 cm