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 experimental 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 should help you to be prepared for a productive experience in lab. Complete this exercise and bring your written 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 refractive index? 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? Be sure 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 where the image is cast. Indicate the two foci, the object distance, the image distance, the object height 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 P4: Lens Optics Rev 2 YJB 15May15 p. 1 / 6
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 The Snell s Law apparatus includes a ray table, a light source, and a sample of transparent plastic in the shape of a semi-circular cylinder. The ray table, shown in Figure 1, is a circular platform with the circumference graduated in degrees of arc essentially a protractor. The light source projects a narrow beam of light across the table in such 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 that the incident ray passes exactly through the center of the arc of the semicircle as shown in Figure 2. In this configuration the incident ray will be refracted at a plane interface while the refracted ray will exit the curved part of the cylinder at normal incidence and not be refracted at that interface. Figure 1: Ray table and D-shaped lens. By varying the angle of incidence on the plane surface of the D-shaped lens, the apparatus may be used to explore the laws of reflection and refraction at a dielectric interface. In order for this apparatus to work correctly it is vital that the D-shaped lens be placed precisely so that the center of the cylinder arc is coincident with the center of the table. The correct footprint of the cylinder is marked on the table surface. The incident light beam must also be aimed precisely at this center point. Good results depend critically on care in positioning the cylinder and the source. Figure 2: Ray table and source. By introducing the light through the cylindrical surface, you can observe the refraction from high index to low index (at the plane surface) and demonstrate the phenomenon of total internal reflection. The source is powered by a wall-wart -style power supply. To turn the source on and off, just plug or unplug the power supply from the source. P4: Lens Optics Rev 2 YJB 15May15 p. 2 / 6 Figure 3: Light source showing ray pattern selector.
As shown in Figure 3 there is a knob on the end of the source that selects different patterns of emitted light beams. You are welcome to experiment with it, but the correct setting for the procedure of this lab is the single slit. Optical Bench The Pasco optical bench provides a convenient means of mounting a light sources, optical elements like lenses, and a screen to investigate the behavior of lenses. The bench includes a built in scale to measure distances among these elements. The light source is the same device as the source for the Snell s Law apparatus. Turned on end it clips to the optical bench and reveals a screen displaying two illuminated arrows with millimeter graduations for determining object height. The opening on the other side from the screen reveals a point source. The lens holders and screen clip easily to the optical bench so that they my be positioned as desired. The holder includes a pointer that indicates the position of the optical element on the distance scale. The source includes two such pointers, one for the screen and one for the point source (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. It includes an objective lens of 420 mm focal length and an ocular lens of 30 mm focal length. A pair of telescoping cardboard tubes and fixtures to allow you to mount lenses in each end to make a telescope. P4: Lens Optics Rev 2 YJB 15May15 p. 3 / 6
Objective and Background The object of this lab is to give you some basic experience with the physics of refraction and with the 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 description of 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 correct alignment of the sample and the incident beam. 2. Devise an experiment to validate Snell s Law and determine the index of refraction of the material of your sample. A good approach is to measure the angle of refraction for several angles of 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 acrylic plastic 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 interface obey the law of reflection? 4. Try projecting the incident beam through the curved surface of your sample. Alignment is still critical! You want normal incidence on the curved surface so that no refraction occurs there. The beam exits through the plane surface and will be refracted and reflected at that interface. Adjust the angle of incidence to observe the critical angle of total internal reflection. Does it occur at the value you expect? 2. Real Images Set up the optical bench with the source at one end and the screen at the other. Place the 100mm or 200 mm lens in the middle of the bench and move it until a sharp image of the source appears on the screen. Using the scale on the bench, determine the object distance and image distance. Using the built-in scale 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 in which the object distance is greater than the image distance, and one for which the image distance is greater than the object distance. Use at least two focal lengths. For each case you try, verify that 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 the image 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 holder taking care to be sure that it is centered properly. Centering is necessary for the paraxial approximation to be appropriate. P4: Lens Optics Rev 2 YJB 15May15 p. 4 / 6
Devise a procedure to measure the focal length of this lens. Execute your procedure and show your results to your TA. 4. The Telescope 1. Before assembling your telescope kit, try this simple experiment. Using the mounted lenses from the optical bench, hold the 250 mm lens in one hand at arm s length. Hold the 100 mm lens right in front of your eye. Try to align the optical axes of the two lenses and move the far lens (the objective) closer to the near lens (the ocular) until objects on a far wall come into focus. You ve built 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 the larger-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 short cardboard spacer tube. Orient it with the plane surface out of the tube. The two large cardboard tubes telescope together. By sliding the ocular tube you can change the distance between the objective 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 this is 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 telescopic image 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 your measured magnification what you should expect? Writeup For your writeup, be sure you complete the following tasks and turn in to your TA a brief account of having done so. 1. Measure the index of refraction of the plastic used to make the D-shaped lens you used to demonstrate 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 the value of the focal length. P4: Lens Optics Rev 2 YJB 15May15 p. 5 / 6
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 procedure and method of data reduction for your validation of Snell s Law. The essential elements are 1. Description of your procedure. 2. Table of data and computations. You may put data and computations in the same table, but be 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 simple estimate 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 include all 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.) P4: Lens Optics Rev 2 YJB 15May15 p. 6 / 6