(Updated April 2024)

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.

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.

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.

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

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,

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.

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).

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.

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. 

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

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.