PHYS 2212 Module 14.2

Spherical Mirrors

14.2 Spherical Mirrors

Learning Objectives

By the end of this section, you will be able to:

Describe image formation by spherical mirrors.
Use ray diagrams and the mirror equation to calculate the properties of an image in a spherical mirror.

Images Formed by Spherical Mirrors

We already briefly discussed how you see an image formed by a flat mirror. Now we will look at images from curved mirrors. You actually see these all the time, but maybe never thought about how they work.

In this picture on the left, a makeup mirror is a concave (converging) mirror. The picture on the right shows a convex (diverging) mirror.

A concave mirror is a curved mirror whose reflective side is on the inside of the curve, like here:

A convex mirror is a curved mirror whose reflective side is on the outside of the curve, like here:

Practice!

Practice 14.2.1
You wish to reflect sunlight from a mirror onto some paper under a pile of wood in order to start a fire. Which would be the best choice for the type of mirror?

Check your answer: A. concave

Practice 14.2.2
The diagram shows three light rays reflected off of a concave mirror. Which ray is NOT correct?

Check your answer: C

Practice 14.2.3
The image produced by a concave mirror of a real object is…

Check your answer: C. sometimes real and sometimes virtual.

Practice 14.2.4
The image produced by a concave mirror of a real object is…

Check your answer: C. sometimes upright and sometimes inverted.

Practice 14.2.5
The image produced by a convex mirror of a real object is…

Check your answer: B. always virtual.

Practice 14.2.6
The image produced by a convex mirror of a real object is…

Check your answer: A. always upright.

Practice 14.2.7
Take a look at this picture of some NASA scientists working on a mirror for a large telescope. Based on the appearance of this image, you would conclude which of the following?

Check your answer: B. The mirror is concave and the image is virtual.

Mirror Equations

The Mirror Equation and Magnification

The mirror equation is:

and the magnification is:

The sign conventions are:

	Converging (Concave) Mirror	Diverging (Convex) Mirror
Real Object	+ d_o	+ d_o
Real Image	+ d_i	N/A (convex mirrors cannot form real images)
Virtual Image	– d_i	– d_i
Focal Length	+ f	– f

Pause & Predict 14.2.1
Where does the image of the apple form, relative to the mirror?

Pause & Predict 14.2.2
What is the magnification of the image of the apple?

Practice!

Practice 14.2.8
When you hold a spherical concave mirror with a 48.2-cm radius of curvature in front of your face, you see an image of your face that is 61.8 cm in front of the mirror. What is the distance between the mirror and your face?

Check your answer: A. 39.5 cm

Practice 14.2.9
When you hold a spherical concave mirror with a 48.2-cm radius of curvature 39.5 cm in front of your face, you see an image of your face that is 61.8 cm in front of the mirror. What is the magnification of this image?

Check your answer: C. -1.56

Practice 14.2.10
When you hold a spherical concave mirror with a 48.2-cm radius of curvature 19.4 cm in front of your face, you see an image of your face in the mirror. Where is this image located, with respect to the mirror?

Check your answer: B. 99.5 cm behind the mirror

Discuss!

An automobile rear-view mirror shows an image of a truck at a time when the truck is 3.0 m from the mirror. The focal length of the mirror is -0.58 m.

(a) Find the position of the image of the truck.

(b) Find the magnification of the image.