University of Puget Sound Introductory Physics Laboratory
9.
Mirrors and lenses
Name:____________________
Date:___________________
Objectives
1. To observe image formation with a variety of mirrors and lenses.
2. To become skilled at analyzing how mirrors and lenses redirect light.
Equipment Optical rails, lens mounts, cardboard screen, light sources, lenses
and mirrors.
Introduction
Last week you observed and quantified the phenomena of reflection, refraction,
and dispersion. This week you will see how these physical processes can lead to
imaging. Refraction in a lens or reflection from a mirror redirects light rays. If
the lens or mirror is shaped correctly, the rays emanating from an object can be
made to intersect at another point, called the image point. The imaging
properties of lenses or mirrors can be simply described without recourse to the
intricate details you studied last week (e.g. the law of reflection or Snell's law).
Instead, a lens or mirror is characterized by its focal length and the imaging
properties described by the thin-lens equation. Today you will investigate how
lenses and mirrors image light and get a feel for ray diagrams and the lens
equation. Next week you will apply this knowledge to construct two basic
optical instruments: the telescope and the microscope.
Lenses
Set up a light source, a thin converging lens, and white cardboard screen
on the optical rail. The light source is our "object," and light rays from it are bent
by passing through the lens. These light rays cross at the "image" position. The
image can be viewed by placing the white cardboard screen at the image
position. Play around with the position of the lens and the screen until you get a
good image on the screen. You can measure the distance from the object and
image to the lens using the ruler on the side of the optical rail. Observe how the
image distance changes when you change the object distance. Which way does
the image move when you move the lens toward or away from the light source?
9-1
For a given object distance, the image distance can be predicted using the thinlens equation (which we will not derive here). The lens equation and an
accompanying diagram will be up on the blackboard. Make a copy of the
diagram and the lens equation in the space below. The magnification is just the
ratio of the apparent size of the image to the actual size of the object. For thin
lenses one can also derive that the magnification equals the negative of the ratio
of the distances of the image and object to the lens.
Note that the lens equation involves the focal length f for the lens, which gives a
measure of how much the lens bends light, (f depends on the lens curvature and
the index of refraction of the glass). What is the image distance di when the
object distance d0 is very large (large compared to the focal length)? What is the
image distance when the object is placed at the focal point? Where should you
place the object so that the image is equally far from the lens?
9-2
Determine the focal length of the converging lens by measuring several object
and image distance pairs and applying the thin lens equation. Also, directly
measure the object and image heights and use them to determine the magnification. Compare with the magnification that would be predicted using the object
and image distances.
object
distance do
image
distance di
image size
hi
calculated magnification
hi/ho
focal length
ratio of
di/do
What happens to a well-focused image when a portion of the lens is blocked?
Does the left side of the image disappear when the left half of the lens is covered?
Or the right half, or what? Explain your observations. Describe what happens
when the object distance is less than the focal length. Can you focus the image
on a card? Can you see the image? If so, describe its properties. Finally, place
the light source at one end of the optical rail and the white cardboard screen at
the other. Notice that there are two lens positions that result in a focused image.
Explain this result by considering the form of the thin-lens equation.
9-3
Plane mirrors
How long must a full-length mirror be? Have a lab partner hold a small plane
mirror flat against the wall and move it up and down. Measure the length a full
size mirror would have to be. Does it matter how far you are from the mirror?
Draw a picture showing the light coming from your feet, reflecting off the mirror
and into your eyes. Do the same for the light coming from the top of your head,
reflecting off of the mirror and into your eyes. From your ray diagram, predict
how long the mirror should be, and compare it to your measured value(s).
Observe the hinged plane mirrors. Notice how the number of images varies as
the angle between the mirrors is changed. Draw ray diagrams to convince
yourself how this works.
9-4
Curved mirrors (Please be careful not to get fingerprints or dirt on these mirrors)
Light a flashlight bulb by connecting it to a battery. This will serve as your
object, as a point source of light. Set the bulb up on the optical axis (the axis of
symmetry of the lens) of a concave mirror, and use a white card to search for the
image of the bulb. Measure the image and object distances, and calculate the
focal length of the mirror using the lens equation.
object
distance d0
image
distance di
calculated
focal length
If you place the bulb inside the focal length of the mirror, you should produce a
"virtual" image. That is, the rays of light reflecting off the mirror appear to come
from a point behind the mirror, instead of in front of it. If you look into the
mirror, you can see the virtual image. But if you place your white card where
you think the image is, you won’t find any light there. It just looks like the light
came from a point behind the mirror. Describe the properties of the real and
virtual images you observed, e.g. are they bigger or smaller, right side up or
upside down.
9-5