Mirrors & Lenses


23.1 Flat Mirrors (also called plane mirrors)






An object viewed using a flat mirror appears to be located behind the mirror, because to the observer the diverging rays from the source appear to come from behind the mirror.





The images reflected in flat mirrors have the following properties:


The image distance q behind the mirror equals the object distance p from the mirror


The image height h’ equals the object height h so that the lateral magnification  


The image has an apparent left-right reversal


The image is virtual, not real!


Real Image  where the light ray actually come to a focus  you can actually see the object projected on a screen placed at that location


Virtual Image  no light rays actually come directly from a virtual image, they just appear to the eye to do so. (When you see yourself in the mirror, are you actually located behind it as you appear?)


To figure out what happens: draw rays, use law of reflection, use geometry





Example: “I can see myself”  how high must the mirror be for the man to see all of himself?



23.2 Images Formed by Spherical Mirrors

Spherical Mirror:


Principle Axis: OCIV


Center of Curvature C


Radius of Curvature R


Light rays converge to a real image at image point  I


Where is the image formed? What is its height?  Draw two rays: one hitting V and the other passing through C:





. We give this location a special name & designation : the focal point . With this designation we can re-write the concave spherical mirror equation as:  


Note, however, that truly spherical mirrors do not bring all rays to focus at the same location!


Spherical Aberration  this is the problem the Hubble Space Telescope had when first launched.


23.3 Convex Mirrors (diverging mirrors) and Sign Conventions



Is the entry for Image location q correct?


Example: Problem #6

A spherical Christmas tree ornament is 6.00 cm in diameter. What is the magnification of an object placed 10.0 cm away from the ornament?



Example: Problem #11

A 2.00-cm-high object is placed 3.00 cm in front of a concave mirror. If the image is 5.00 cm high and virtual, what is the focal length of the mirror?


Example: Problem #16

A convex spherical mirror with a radius of curvature of 10.0 cm produces a virtual image one-third the size of the real object. Where is the object?


23.5 Atmospheric Refraction (read)


23.6 Thin Lenses

Note: a convex-concave lenses is sometimes referred to as a meniscus. It is the shape used for most eyeglasses.


Using the same sign convention for thin lenses:






Same as for mirrors!

(This is the thin lens equation)





If you are on a computer with Java installed go here and play with the mirrors & lenses. If it doesn’t fire up after a few seconds, go down to “8” and hit the start button. These little applets will give you a “feel” for what happens. Also try this converging lens and diverging lens applets. Simpler & prettier (but no mirrors).

Example: Problem #32


A convex lens of focal length 15.0 cm is used as a magnifying glass. At what distance from a postage stamp should you hold this lens to get a magnification of +2.00?


Example: Problem #36


An object’s distance from a converging lens is ten times the focal length. How far is the image from the focal point? Express the answer as a fraction of the focal length.


Multiple Lenses


This is more complicated, but straightforward if you follow these rules:


  1. Do the first lens as if the others weren’t there.


  1. Use the image formed by this lens as the object of the next lens


  1. Repeat this process for all the lenses in the system


  1. The total magnification is just the product of the individual magnifications of each lens.


See Example 23.9 of the book


Example: Problem #41


Two converging lenses, each of focal length 15.0 cm, are placed 40.0 cm apart, and an object is placed 30.0 cm in front of the first. Where is the final image formed, and what is the magnification of the system?



Microscope: Object very close to F0 makes a real inverted larger image. This image is then viewed & magnified further using the eyepiece.


Telescope: Object near infinity forms a real inverted smaller image near the focal point. Eyepiece is used to magnify this image.

The angular magnification (how much bigger it looks) is just . To get different magnifications, just change eyepieces!









Most large telescopes use a concave mirror instead of a lens to form the image.