University of Puget Sound Introductory Physics Laboratory
8.Reflection, refraction, and dispersion
Name:______Date:______
Objectives
1. To observe and quantify the basic phenomena of geometrical optics, including reflection, refraction and dispersion.
2. To anaylze experimental observations in terms of a simple model to determine the functional form of a model parameter.
Equipment
Light ray box, plastic lenses, water lenses, mirrors, protractor, and ruler.
Introduction
In an earlier lab session you observed a variety of different wave phenomena occurring with water waves in the ripple tank. There are some phenomena, like diffraction, that are only observable when the wavelengths involved are about the same size as the objects that the waves encounter. For example, x rays diffract from crystals because the wavelength of the x rays and the spacing between the atoms in a crystal are about the same, a few tenths of a nanometer (roughly the "size" of an atom). The wavelength of ordinary light is about a half of a micron. That's big enough that we can make obstacles like pinholes and slits which will diffract light. However, most obstacles that light encounters in ordinary life - mirrors, lenses, water droplets, doorways - are large enough that diffraction is negligible. In this limit, where the wavelength is much smaller than the obstacle size d, we can use geometrical optics. Geometrical optics is particularly simple: the wave travels along ray trajectories, without getting mixed up and interfering with itself. To understand how glass lenses or curved mirrors work with geometrical optics, one simply has to figure out how the object alters the light ray trajectories. Today you will examine the general phenomena of reflection, refraction and dispersion in the limit of geometrical optics. In a later lab session you will experiment with mirrors and lenses to see how these phenomena lead to imaging.
Procedure
Before you is a light ray box with a collimating lens and a plastic end slide that has several different apertures in it. With the unit unplugged, pull it apart and inspect it. Once you are satisfied, reassemble it, insert the end slide and turn on the light. If you set the ray box down on white paper the ray(s) of light will be more visible. You can collimate (make parallel) several rays from the light box by adjusting its length. You now have a neat tool to investigate how different obstacles can alter the trajectory of light rays.
Reflection
Previously you saw that a plane water wave bounced off of a large, flat obstacle like a billiard ball. Large compared to what? Does a beam of light act the same way? Check it out. Use a single light ray to observe reflection from a plane mirror. Is the incident angle always equal to the reflected angle? Trace the light rays on the paper and measure several angles to check it out. Does it also work for curved mirrors? Try using your single light ray to observe reflection from both concave and convex mirrors. Again trace the rays on the paper and measure one angle for both types of mirrors. How are you defining the angle you are measuring? In the space below answer the above questions and sketch the three cases.
Next, observe reflection in the same three mirrors using five rays simultaneously. Aha! Draw pictures and describe what the three mirrors do to the light rays when they are directed straight into the mirror (along the axis of symmetry). For the convex mirror, trace the trajectories backwards behind the mirror to find the intersection point of all the rays. If you ignore the mirror, it looks like the light is all coming from this point. Try sending the rays in at different incident angles. How does this affect the reflected trajectories? For the concave mirror, at what incident angle is the focus the sharpest?
When you send parallel light straight into the concave or convex mirrors, the reflected light rays intersect at the focal point. The focal length of the mirror is the distance from the focal point to the mirror surface. This length characterizes the imaging properties of the mirror, and it of course depends on the curvature of the mirror surface. You can determine the radius of curvature of the concave mirror surface by tracing the paths of several single light rays that strike the mirror at normal incidence. The local normal changes direction since the mirror is curved, so you'll have to direct the ray in at different spots on the mirror and adjust the incident angle to be normal at each spot. This set of lines should intersect at the center of curvature, right? Measure and quote the radius of curvature for both the concave and convex mirrors. You can also simply determine the focal length of both mirrors using the five collimated rays. Measure and quote the focal length of each mirror. What is the relationship between the focal length and the center of curvature?
Index of refraction
Mirrors reflect light. Light rays bounce off the mirror according to the law of reflection, making equal angles to the local normal. It's the shape of the mirror that determines where the light goes. Glass or plastic lenses refract light. To understand how lenses work we first investigate how refraction works. As you saw earlier, when a wave enters a region where it travels at a different speed, the direction of the wavefront changes. The speed of light in glass is slower than it is in air, so light rays entering a lens bend and change direction. The amount of bending of the light ray depends on the incident angle and how much the wave slows down. So for refraction it is both the shape and the nature of the lens material that determines where the light goes.
Shine a single ray from the light box through the clear plastic piece with parallel sides. Vary the incident angle from normal to grazing incidence. Notice that the light comes out displaced but remains nearly parallel to the incident ray. It bends one way going into the plastic, and then bends back the same amount when it leaves. Which way (relative to the normal) does the light bend when it enters plastic? Which way does it bend when it exits the plastic? Does it work this way over the whole range of incident angles?
Trace the path of the incident and refracted light rays (the rays in the plastic) for six different incident angles. Yes, six. Should you pick the set of incident angles close together or far apart? In each case measure the angle of the rays with respect to the normal to the surface, and record them in the table below. Be sure to measure them from the normal and not from the surface.
incident angle i / refracted angle r / sin(i) / sin(r) / sin(i)/sin(r)At first glance there doesn't seem to be a simple relationship between the angles. There is a relationship that can be derived called Snell's law(ask your instructor, or check out a textbook if you are interested). Snell's law relates the incident and refracted angles to the indices of refraction, denoted by n, of the two media. Snell's law states that
where ni and nr are the refraction indices in the two media (air and plastic). The index of refraction tells you how much the wave slows down in that medium. For light, the speed in vacuum is c = 3.00x108 m/s. In a medium with a refractive index n the speed is v=c/n. Air doesn't slow down light very much, so the index of refraction for air is very nearly equal to one.
Fill in the last three columns of the table and use Snell's Law to obtain six values for the index of refraction for the plastic. Quote a mean value for the refraction index, as well as the uncertainty in the mean. (If need be, refer to the appendix on quick and dirty statistics). Is the measurement more accurate near normal incidence, or near grazing incidence, or where?
Repeat this index of refraction determination using the rectangular water container. Report both a mean value and the uncertainty in the mean value for the refraction index of water.
incident angle i / refracted angle r / sin(i) / sin(r) / sin(i)/sin(r)Dispersion
Different colors of light (different wavelengths) can travel at different speeds through matter. Put another way, the index of refraction of a material can and typically does depend on the wavelength. That means that the different colors present in a light beam will bend different amounts as they cross an interface between media with different refractive indices. Prisms make rainbows. This phenomena is called dispersion. There can be useful physical information in the spectra of light that can tell us much about the source of light, and being able to disperse light to examine the different colors that are present is a powerful tool.
To make a rainbow you need to use something clear that doesn't have parallel sides. Try using the plastic prism to break a single ray of white light into its spectrum of colors. It’s easier to see in the dark. Vary the incident angle and try to get the rainbow to fan out. Trace an outline of the prism and the entering ray and exiting bundle of rays. Indicate which colors you see and in which order they appear. Which color is bent the most? Which color travels the fastest through the plastic?
Talk with your lab mates about what this observation tells you about the index of refraction. Does the index increase or decrease with wavelength? Construct a rough graph of how you think the index of refraction varies with the wavelength of light. On the horizontal axis put wavelength ranging from blue to red. Put the index of refraction on the vertical axis. By how much do you think the index varies over the wavelength range from blue to red? How could you estimate this?
Before you leave:
Tell your instructor how you determined the uncertainty in the mean value of the refractive index for water.
Show your instructor your final graph, and make an argument for your prediction for the variation of the index of refraction of the plastic over the visible light range.
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