The Lens Equation
Introduction
When light is incident on a boundary between two media, part of the light is reflected and part is
refracted. When light is incident on a mirror, nearly all of it is reflected. When light is incident on a
lens, nearly all of it is refracted (bent). The study of these macroscopic properties of light is called
geometric optics or ray optics. Light rays and the laws of reflection and refraction can be used to analyze the
behavior of light when it comes in contact with one of these devices.
We can also use the thin lens equation to make predictions:
1/f = 1/s + 1/s’
f = focal length = distance between lens and location parallel rays converge
s = object distance = distance between object (light source) and lens
s’ = image distance = distance between lens and image
Be very careful with signs in this equation. The object distance, s, is always positive for a single lens.
The image distance, s’, is positive if the image is on the opposite side of the lens as the object.
Otherwise, s’ is negative. If a lens focuses parallel light rays to a point, then the focal length of a device
is considered positive. This is typically a biconvex lens. If a lens causes parallel light rays to diverge,
then the focal length is considered negative. This is typically a biconcave lens.
The purpose of this lab is to test the lens equation.
Experimental Procedures
Measuring the Object Height and Focal Lengths
Note that this is the most important part of this experiment. These measurements will severely impact
the quality of your entire experiment, so be especially careful here.
1) Measure the height of the light source (the diameter of the circle). This is the object height, h.
2) Place the light source extremely far away (across the room) from a bi-convex lens. Don’t be lazy.
GO ALL THE WAY ACROSS THE ROOM! If you or your lab partners decide to be lazy during
this step, then you will get the wrong focal lengths and your entire experiment will be worthless.
Another option is to use the sun as the source of light, weather permitting.
3) Place a biconvex lens in a holder and put it on a rail. Place a card in a holder and put it on the same
rail.
4) Move the manila card until the light focuses on a point. The distance between this point and the
lens is the focal length.
5) Repeat steps 3 and 4 with four other bi-convex lenses.
6) Note any relationship between the physical construction of the lenses and their focal lengths.
7) Select three lenses. The lenses should have focal lengths between 6 and 32 cm and be significantly
different from one another. Keep track of these three lenses.
Experimental Image Distances, Image Heights, and Magnifications
1) Choose a lens from the three of known focal length.
2) Choose an object distance so that 1.2*f < s < 4*f. Place the object at one end of the optical rail.
Place the lens at the chosen object distance, s, from the object.
3) Move the card in its holder until the image is in focus on the opposite side of the lens. You may
need to add a second rail if you run out of room. Do not move the lens or the object. The image
should be in focus, but there might be a range of distances for which the image appears to be in
focus. The distance from the card to the lens is the image distance, s’. Independently evaluate the
error estimation for the image distance every time you measure it since the error might vary.
4) Measure the image height, h’, the diameter of the circle. If it is inverted with respect to the object,
then the image height is considered negative by convention. Calculate the experimental
magnification using the definition m = h’/h. Note that this is a dimensionless quantity.
5) Repeat steps 2 through 4 with a different object distance. Use at least five significantly different
object distances for a particular lens. The object distances should always be greater than 1.2*f and
less than 4*f.
6) Repeat steps 1 through 5 with the other two lenses.
Blocking Light
1) Leave one of the images in focus. What do you think will happen to the image if you cover up half
of the lens (dimmer, half image, out of focus, something else)? What will happen if you cover up
half of the object?
2) Test your predictions.
Theoretical Image Distances and Magnification
1) Solve the lens equation for s’. The symbols s and f should only appear once in your equation.
2) Using this equation, calculate s’ based on experimental s and f. Record the results in three tables,
one for each lens.
3) Using these results, graph experimental and theoretical s’ (on the vertical axis) as a function of s (on
the horizontal axis) for each of the three lenses. Show your graph to your instructor.
4) Is the lens equation supported by your experiment?
5) Calculate the theoretical magnification using the formula m = -s’/s. Use the theoretical image
distance.
6) Using these results, graph experimental and theoretical m (on the vertical axis) as a function of s (on
the horizontal axis) for each of the three lenses. Show your graph to your instructor.
7) Is the magnification equation supported by your experiment?