PHYS 1112 Module 16.2

Spherical Mirrors

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 16.2.1
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 16.2.2
The diagram shows three light rays reflected off of a concave mirror.

Which ray is NOT correct?
Check your answer: C
Practice 16.2.3
The image produced by a concave mirror of a real object is…
Check your answer: C. sometimes real and sometimes virtual.
Practice 16.2.4
The image produced by a concave mirror of a real object is…
Check your answer: C. sometimes upright and sometimes inverted.
Practice 16.2.5
The image produced by a convex mirror of a real object is…
Check your answer: B. always virtual.
Practice 16.2.6
The image produced by a convex mirror of a real object is…
Check your answer: A. always upright.
Practice 16.2.7
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) MirrorDiverging (Convex) Mirror
Real Object+ do+ do
Real Image+ diN/A (convex mirrors cannot form real images)
Virtual Image– di– di
Focal Length+ f– f
Pause & Predict 16.2.1
Where does the image of the apple form, relative to the mirror?
Pause & Predict 16.2.2
What is the magnification of the image of the apple?

Practice!

Practice 16.2.8
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 16.2.9
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 16.2.10
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.