Physics 4 Laboratory

Snell’s Law, Lenses, and Optical Instruments

Prelab Exercise

Please read the Procedure section and try to understand the physics involved and how the exper-imental procedure works. You will be provided with equipment to explore the laws of refraction,how lenses work, and how to use them to make simple instruments. The questions below shouldhelp you to be prepared for a productive experience in lab. Complete this exercise and bring yourwritten responses to lab with you.

1. What is meant by the optical index of refraction of a material?

2. Why does light refract at an interface between two transparent media of different refractiveindex? Include a sketch as part of your response.

3. What is Snell’s Law of Refraction? Include a diagram to clarify your response.

4. Does light obey the Law of Reflection at the interface between two transparent media? Besure to include the reflected ray in the diagram for the previous question.

5. When does total internal reflection occur?

6. What is meant by the focus of a lens?

7. What is meant by the focal length of a lens?

8. How can a lens have a negative focal length? (Be sure to use the words “converging” and“diverging” in your response.

9. Draw a ray diagram for a positive thin lens with the object outside the focus. Show wherethe image is cast. Indicate the two foci, the object distance, the image distance, the objectheight and the image height. Draw and label the three principle rays.

Equipment

• Pasco 1-m optical bench

• Pasco screen

• Pasco optical light source

• Pasco lens holder

• Lens of unknown focal length

• Mounted lens f = +250 mm

• Mounted lens f = +200 mm

• Mounted lens f = +100 mm

• Ruler

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• Pasco ray table

• Pasco D-shaped lens

• Learning Technologies PS-04B Refracting Telescope kit

• LED table lamp or flashlight

• Telescope target

Snell’s Law Apparatus

Figure 1: Ray table and D-shaped lens.

The Snell’s Law apparatus includes a “ray table,” a lightsource, and a sample of transparent plastic in the shape ofa semi-circular cylinder. The ray table, shown in Figure1, is a circular platform with the circumference gradu-ated in degrees of arc—essentially a protractor. The lightsource projects a narrow beam of light across the table insuch a way that part of the beam falls on the table surface,thus illuminating the path of the ray. The half-cylinder—called a “D-shaped lens”—is placed on the table so thatthe incident ray passes exactly through the center of thearc of the semicircle as shown in Figure 2. In this con-figuration the incident ray will be refracted at a planeinterface while the refracted ray will exit the curved partof the cylinder at normal incidence and not be refractedat that interface.

Figure 2: Ray table and source.

By varying the angle of incidence on the plane surfaceof the D-shaped lens, the apparatus may be used to ex-plore the laws of reflection and refraction at a dielectricinterface.

In order for this apparatus to work correctly it is vitalthat the D-shaped lens be placed precisely so that thecenter of the cylinder arc is coincident with the center ofthe table. The correct footprint of the cylinder is markedon the table surface. The incident light beam must alsobe aimed precisely at this center point. Good results de-pend critically on care in positioning the cylinder and thesource.

Figure 3: Light source showing ray pat-tern selector.

By introducing the light through the cylindrical surface,you can observe the refraction from high index to lowindex (at the plane surface) and demonstrate the phe-nomenon of total internal reflection.

The source is powered by a “wall-wart”-style power sup-ply. To turn the source on and off, just plug or unplugthe power supply from the source.

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As shown in Figure 3 there is a knob on the end of the source that selects different patternsof emitted light beams. You are welcome to experiment with it, but the correct setting for theprocedure of this lab is the single slit.

Optical Bench

The Pasco optical bench provides a convenient means of mounting a light sources, optical elementslike lenses, and a screen to investigate the behavior of lenses. The bench includes a built in scaleto measure distances among these elements.

The light source is the same device as the source for the Snell’s Law apparatus. Turned on end itclips to the optical bench and reveals a screen displaying two illuminated arrows with millimetergraduations for determining object height. The opening on the other side from the screen revealsa point source.

The lens holders and screen clip easily to the optical bench so that they my be positioned asdesired. The holder includes a pointer that indicates the position of the optical element on thedistance scale. The source includes two such pointers, one for the screen and one for the pointsource (which is somewhat behind the surface of the device).

Figure 4: Optical bench with light source, mounted lens, lens holder, and screen.

Telescope Kit

The telescope kit includes the key components to assemble a low-power astronomical telescope. Itincludes an objective lens of 420 mm focal length and an ocular lens of 30 mm focal length. A pairof telescoping cardboard tubes and fixtures to allow you to mount lenses in each end to make atelescope.

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Objective and Background

The object of this lab is to give you some basic experience with the physics of refraction and withthe use of lenses to make optical instruments.

Procedures

As always, be sure to keep records of what you do so that you can prepare a coherent descriptionof your findings. Feel free to explore beyond the procedures described.

1. Snell’s Law

1. Familiarize yourself with the operation of the apparatus and notice the sensitivity to correctalignment of the sample and the incident beam.

2. Devise an experiment to validate Snell’s Law and determine the index of refraction of thematerial of your sample. A good approach is to measure the angle of refraction for several anglesof incidence and make a table of this data. Make the assumption that the index of air is n = 1.00.A simple computation should give you many individual measurements of the index of the acrylicplastic used in the D-shaped lens. How would you determine the precision of your measurement?Describe your technique to your TA.

3. As part of this experiment, also collect data on the reflected beam. Does the dielectric interfaceobey the law of reflection?

4. Try projecting the incident beam through the curved surface of your sample. Alignment is stillcritical! You want normal incidence on the curved surface so that no refraction occurs there. Thebeam exits through the plane surface and will be refracted and reflected at that interface. Adjustthe angle of incidence to observe the critical angle of total internal reflection. Does it occur at thevalue you expect?

2. Real Images

Set up the optical bench with the source at one end and the screen at the other. Place the 100mmor 200 mm lens in the middle of the bench and move it until a sharp image of the source appearson the screen.

Using the scale on the bench, determine the object distance and image distance. Using the built-inscale on the source determine the object height. With a ruler, measure the image height.

Repeat this procedure for at least four configurations. Be sure to include one configuration inwhich the object distance is greater than the image distance, and one for which the image distanceis greater than the object distance. Use at least two focal lengths. For each case you try, verifythat the image distance, object distance, image height and object height correspond appropriately.

If you remove the screen, can you position your eye to see the image? What is the location of theimage you are seeing?

3. Measuring the Focal Length

You will be provided with a (positive) lens of unknown focal length. Mount it in the lens holdertaking care to be sure that it is centered properly. Centering is necessary for the paraxial approxi-mation to be appropriate.

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Devise a procedure to measure the focal length of this lens. Execute your procedure and show yourresults to your TA.

4. The Telescope

1. Before assembling your telescope kit, try this simple experiment. Using the mounted lenses fromthe optical bench, hold the 250 mm lens in one hand at arm’s length. Hold the 100 mm lens rightin front of your eye. Try to align the optical axes of the two lenses and move the far lens (theobjective) closer to the near lens (the ocular) until objects on a far wall come into focus. You’vebuilt a telescope! Is the image erect or inverted? Is it magnified?

2. Assemble your telescope. As shown in Figure 5 the objective lens is held onto the end of thelarger-diameter tube with the red cap. Orient it with the curved surface pointing out of the tube.The ocular lens is held in the end of the narrower tube by the piece of foam stiffened with the shortcardboard spacer tube. Orient it with the plane surface out of the tube. The two large cardboardtubes “telescope” together. By sliding the ocular tube you can change the distance between theobjective and ocular, thus focusing your telescope.

Figure 5: Exploded view of telescope showing configuration of parts.

3. Use the telescope to observe and describe a target described to you by your TA.

4. Devise a method of estimating the angular magnification of your telescope. One way to do thisis to observe a target simultaneously with one eye through the telescope and the other without.With a little care and concentration you can see both the “naked-eye” image and the telescopicimage simultaneously. You can then compare their apparent sizes.

The focal length of the objective is 420 mm. The focal length of the ocular is 30 mm. Is yourmeasured magnification what you should expect?

Writeup

For your writeup, be sure you complete the following tasks and turn in to your TA a brief accountof having done so.

1. Measure the index of refraction of the plastic used to make the D-shaped lens you used todemonstrate Snell’s Law.

2. Show that the critical angle for total internal reflection occurs at the expected value.

3. Describe your method of determining the focal length of the unknown lens and determine thevalue of the focal length.

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4. Observe and describe the telescopic target.

5. Estimate the angular magnification of your telescope.

6. Carefully disassemble your telescope.

7. Turn off all electrical equipment.

Homework

For the homework portion of this lab exercise, prepare a brief, simple report describing your pro-cedure and method of data reduction for your validation of Snell’s Law. The essential elementsare

1. Description of your procedure.

2. Table of data and computations. You may put data and computations in the same table, butbe sure to indicate clearly what is measured and what is computed.

3. Description of data reduction procedure. Be sure to explain the theoretical justification.

4. Give a conclusion about whether or not your results confirm Snell’s Law. Include a simpleestimate of precision (a standard deviation will do).

This report should be quite brief and straightforward to prepare—probably about three pages.Collaborate with your lab partners in preparing it and submit a single report. (Be sure to includeall authors’ names.) Please do type your report. You may hand-draw any figures, but be neat!.

Do not fail to cite your sources as appropriate. (See the syllabus.)

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