Geometrical Optics PHYS143

(Updated April 2024)

This lab is intended to illustrate how light rays behave in some simple optical setups.


The term geometrical optics refers to the study of light propagation in the limit as the wavelength of light is much smaller than any of the optical components of the system, e.g., apertures, lenses, or mirrors. Another simplifying assumption is that each medium through which the light travels (e.g., air, water, glass) is homogeneous and that all changes between media are abrupt at the interfaces. A consequence of these assumptions is that light travels in straight lines through each medium and that changes in the direction the light travels occur only at the interfaces between media. The direction light travels is conveniently described by the term rays.

Lab notebook template

One member of the group should click on the link below to start your group lab notebook. (You may be asked to log into your UChicago Google account if you are not already logged in.) Make sure to share the document with everyone in the group (click the “Share” button in the top right corner of the screen) so each member has access to the notebook after you leave lab. Choose one member of your group to be the designated record-keeper.

The record-keeper role will rotate each week so that everyone gets a chance at it. If a group has three students and does six weeks of lab, then each group member is expected to be record-keeper twice during the quarter.

Part 1 - Reflection, Refraction and Snells Law

Law of reflection

When light strikes a mirror and reflects from its surface, the angle of reflection is equal to the angle of incidence, both angles being measured from the normal to the mirror surface. Also, the incident ray, the reflected ray and the normal to the surface all lie in the same plane.

Law of refraction (Snell's law)

When light passes from one transparent medium into another, in general the light will change speed at the interface between the two media. This change in speed is accompanied by a change in direction or refraction of the light. The angle through which the light changes direction depends on the angle of incidence at which the light strikes the surface and a characteristic of the media at the interface.  This characteristic is known as the index of refraction, n, which is defined as

$n = \dfrac{c_{vaccum}}{c_{medium}}$ (1)

where $c_{vacuum}$ is the speed of light in a vacuum and $c_{medium}$ is the speed of light in the medium.

The relationship between the direction of travel of light and the indices of refraction of the media is known as Snell's law,

$n_1\sin\theta_1 = n_2\sin\theta_2$ (2)

where the angles $\theta_1$ and $\theta_2$ are measured between the light rays and the normal to the surface in each medium. You will verify Snell's law experimentally.

Measure the Index of Refraction of Water and Glass

For each index of refraction (both glass and water) perform the measurements for as many different angles as there are members in your group. This will ensure that everyone has a chance to make some of the physical measurements, and to provide a check on your measurement techniques. There is some judgement on the part of the experimenter as to exactly where to mark the lines which show the rays entering, passing through and leaving the object being measured. One way to test for consistency is to perform the measurement for multiple angles and with different people making the measurement.

  • Find the index of refraction ($n$) for tap water.
  • Find the index of refraction ($n$) for block glass.
  • Using the piece of glass test whether or not the angle of reflection is equal to the angle of incidence.
Note the use of steel pins pressed into the cork board to hold both the laser and the glass (water tray) in place during the measurement.

(Assume the index of refraction of air is 1.0).

Part 2 - Lenses, Images and Telescopes

Simple Lenses - focal point, focal length, and images

When reflecting or refracting materials like mirrors or clear glass are shaped in special ways, they can be used to re-direct light to form images. If the reflecting or refracting surfaces are spherical, this geometry (together with the laws of reflection and refraction) give rise to the ray diagrams illustrated in Fig 1. The lenses shown in Fig 1 are considered thin lenses for simplicity and it is assumed that all of the refraction takes place at the center of the lenses.

Figure 1: Parallel light rays entering from the left, striking lenses and mirrors, and continuing on. The focal points (fp) and focal lengths (f) are shown.

Note that the double convex lens and the concave mirror of Figs. 1(a) and 1(b) redirect the light so that the light rays converge at the focal points. Images formed in this way are called real images, since light actually passes through them.  Real images can be projected onto a screen. 

Note also that the double concave lens and the convex mirror of Figs. 1(c) and 1(d) cause the rays to diverge. Images formed this way must be inferred by extending the light rays back to where they appear to have come from as the dashed lines show. Since no light actually passes through these images they are referred to as virtual images and they cannot be projected onto a screen.

The magnification of a lens or mirror is defined as the ratio of the image diameter to the object diameter.

The Lens Equation

A consequence of the laws of reflection and refraction and the spherical shape of the mirror or lens surface is the relationship

$\dfrac{1}{f} = \dfrac{1}{OD} + \dfrac{1}{ID}$ (3)

where $f$ is the focal length, $OD$ is the object distance (the distance from the object to the lens or mirror), and $ID$ is the image distance (the distance from the lens or mirror to the image). It is remarkable that Eq. (3) applies both to mirrors and lenses with spherical surfaces even though the physics of refraction and reflection is quite different.

Measure the focal lengths of your lenses

Set up the apparatus as shown in Fig. 7.

Figure 7: Optical bench with light source, lens, and projection screen

Estimate the focal length for each of your two lenses. Move the lens and plastic screen along the optical rail until a sharp image is formed on the screen. Note that there is an infinite number of such configurations which will produce images.

A more direct measurement of the focal length may be made by observing the image formed by a distant object. Use a distant light source to form an image on some convenient surface. 

Note that you need two lenses with different focal lengths for your telescope. One of your lenses should be about twice the focal length of the other. If your two lenses have the same focal length, one of your lenses has gotten mixed up with those of another group and you will need to figure out which group has one of your lenses and vice versa.

You will need to keep track of which lens is which for the next part of the procedure.


The basic definition of a telescope can be stated as follows.

The objective lens creates an image of the object. The eyepiece is then positioned to magnify the image created by the objective lens. Figure 11 is a ray diagram of this statement.

Figure 11: (top) Telescope apparatus, (bottom) telescope magnification ray diagram

The longer focal length lens will be the objective of your telescope while the shorter focal length lens will serve as the eyepiece.

Construct a telescope and estimate its magnification.

Arrange the two lenses, light source and screen as shown in the top portion of Fig. 11. First use the longer focal length lens (objective lens) to form the sharpest possible image of the light source on the ground plastic screen. From your measurement of the focal length of this lens you should know where to place the screen to achieve focus.

Then place the shorter focal length convex lens (eyepiece) to act as a magnifier of the image on the screen. Again, from your measurement of the lens's focal length you should know where to place it relative to the image on the screen.

Now place the screen directly in front of the light source which should be set to the circular opening. Look through the eyepiece and you should see the scale on the screen at least close to being in focus. You may have to slightly adjust the position of the “eyepiece” lens to achieve the best focus of the scale on the screen. You should see a magnified image of the scale on the screen.

Report: Summary and Calculations

After the lab you will need to write up and submit your calculations for first part of the lab, the indices of refraction for glass and water and the reflection measurements. This should be a separate document, and it should be done individually (though you may talk your group members or ask questions). Include data for all of the measurements performed, not just the data you took. Show your calculations including uncertainties for each measurement.

The conclusion is your interpretation and discussion of your data. What do your data tell you? How do your data match the model (or models) you were comparing against, or to your expectations in general? (Sometimes this means using the $t^{\prime}$ test, but other times it means making qualitative comparisons.) Your conclusions should always be based on the results of your work in the lab. It is not acceptable to evaluate the results of an experiment by comparison to known values or any other form of preconceived expectation. Your conclusions need to be supported by your data. If your data are inconclusive or in disagreement with regard to your expectations then your conclusion should reflect that.

You do not need to do any calculations nor write anything about the second part of the lab on lenses and the telescope.

REMINDER: Your report is due 48 hours after the lab. Submit a single PDF on Canvas.