3. 3 EQUIPMENT 49 3.3 Equipment Figure 3.14: Equipment setup for Week 3. The following equipment is to be set up at all 11 stations. 1- Optical bench 10- Lab jack 2- 12\" ruler 11- Laser (unused but leave for week 4) 3- (3) Lens holders 12- Sample holder w/ paper 4- (3) Carriages 13- Holed black plate 5-Plane mirror 14- Meter stick 6- Concave lens: f= xx em (red rim) 15- Lit image 7- Convex lens: f= xx cm (blue or black rim) 16- Desk lamp 8- Convex lens: f= xx cm (green rim) 9- Convex lens: f= xx cm (red rim) 50 WEEK 3. LENSES 3.4 Thin lens equation Goal: Measure the focal length and lateral magnication of a convent: lens. Place the red biconvex lens on the optical bench in a lens mount. Mount the lit object in a lens holder at one end of the bench. Adjust the height and orientations of your holders so that the lens and object lie along the same axis, parallel to the optical bench. Slide the lens so that it is 20 cm from the object. Place the white screen in a lens holder on the opposite side of the lens. Move the screen back and forth until the image appears. Is the image upright or inverted? On graph paper, make a scale drawing5 like Fig. 3.2 that shows the three principal rays and the relative positions of the object and the image for your actual measurement. Use the plastic ruler to measure the actual size of the arrow on the lit object and the size of the image on the white card. Make a table with the following headings: 0 (cm), 2' (cm), f (cm), Measured magnication, and 71/0. Complete this table for three values of 0 that are larger than the focal length.6 Examine the data in your table. Does the thin lens equation (Eq. 3.3) give the same value of f for different values of o? Is the measured magnification consistent with the predicted magnication (Eq. 3.4)? 3.5 Autocollimation Goal: Measure the focal length of a convex lens using autocolllmatlon. Mount the black plate with a \"pinhole\" at one end of the optical bench, at the end that is closest to the aisle. Adjust the desklamp to shine through the pinhole. (This arrangement approximates a point source of light.) Put the red biconvex lens approximately one focal length from the pinhole. Hold or mount the plane mirror just beyond the lens. Align the pinhole, lens, and plane mirror so that they are all at the same height and so the mirror and lens are normal to the optical axis. Adjust the lens and mirror position until 5Make the horizontal dimensions to scale. You may use an expanded vertical scale for clarity. 6Make your variations substantial (more than a few centimeters). Include values with i o. 3.6. EFFECT OF RADIUS ON FOCAL LENGTH 51 you see a sharp reected image of the point source in the plane of the point source. The distance from the pinhole to the lens is the focal length. Sketch the rays for this measurement. Show the instructor your measurement and ask him or her to initial your sketch. Is the focal length measured using this technique close to the focal length found previously (in Sec. 3.4)? 3.6 Effect of radius on focal length Goal: Relate the radius of the lens to its focusing properties. Use whichever technique you prefer to measure the focal length of the other two convex lenses. Include the color coding with your data. Make a sketch of two lenses: one thick one with a lot of curvature and one thin (nearly at) one. On each sketch, draw a ray that clearly shows why one lens has a shorter focal length than the other. Be sure that the refracted rays you draw bend at each interface as required by Snell's law (like Fig. 3.5, not like Fig. 3.4). Also explain mathematically why your observations are consistent with the prediction of Eq. 3.2. 3.7 Concave lens Goal: Qaatitativety eramine the properties of a concave tens. Using the apparatus of Sec. 3.4, replace the convex lens with a concave lens. Search for an image with the white card. Also look through the lens at the lit object. Explain your ndings with a sketch of the principal rays and lens. 3.8 Magnifying glass Goal: Use a connect: lens as a simple magnier. Replace the concave lens with a 5 cm diameter convex lens of relatively short focal length. While looking through the lens at the lit object, adjust the position of the lens to obtain a focused image. For what values of 0 do you observe a sharp, upright image? When is the image largest? Sketch the lens and the principal rays. 52 WEEK 3. LENSES 3.9 Refractory astronomical telescope Goal: Assemble a simple astronomical telescope. Remove the screen. Select a moderate focal length convex lens as the objective lens of your telescope and a shorter focal-length lens as the ocular (eyepiece) lens. Place a meter stick on the opposite side of the room and orient your bench to point at it. Adjust the position of your ocular lens until you see a magnied image. Is the image erect or inverted? Adjust the position of the eyepiece and of your head to achieve the maximum magnication consistent with a sharp focus. Also look at the meter stick directly and make a very rough estimate of the effective angular magnication. Compare with the expected value. On graph paper, make a scale drawing like Fig. 3.11 that shows two rays, the relative positions of the lenses, the intermediate image, and your eye for your actual measurement. Show your instructor your setup and ask him or her to initial your drawing. 3. 10 Microscope Goal: Assemble a simple microscope. Select two of your convex lenses and assemble the microscope of Fig. 3.12. Use the lit image on the end of your optical bench as the object. Compare the apparent size of the lit object as viewed through the microscope with the apparent size when viewed directly and make a rough estimate of the effective angular magnication. On graph paper, make a scale drawing like Fig. 3.12 that shows two rays, the relative positions of the lenses, the intermediate images, and your eye for your actual measurement. Show your instructor your setup and ask him or her to initial your drawing