Physics 263 Experiment 7 Geometric Optics In this laboratory, we will perform several experiments on geometric optics. A pictorial diagram of the various components to be used is shown in Figure 5. 1 Refraction When light with a well-defined direction passes between two transparent media, the light is bent (refracted). The Law of Refraction states that n 1 sinθ 1 = n 2 sinθ 2 (1) where n 1 is the index of refraction of medium 1, θ 1 is the angle between the light direction and the normal to the plane, in medium 1 etc. This, and the apparatus setup is shown in Figure 1. Figure 1: Light refraction.
1. Place the ray box on a white sheet of paper on the table. Slide the ray mask until only one white ray is showing. 2. Place the rhombus on the table and position it so the ray passes through the parallel sides as shown in Figure 1. 3. Mark the position of the parallel surfaces of the rhombus and trace the incident and transmitted (refracted) rays. Mark where the ray enters and leaves the rhombus. Draw the normal to the surface. 4. Remove the rhombus and on the paper draw a line connecting the points where the ray entered and left the rhombus. 5. Measure the angles of incidence and refraction with a protractor. Record the data in a spreadsheet. 6. Repeat this procedure for a total of three different angles of incidence. 7. Plotsinθ 1 vs. sinθ 2 anddeterminetheslope. Sincemedium1isair,n 1 1.00,sothe slope is n 2, the index of refraction of the acrylic plastic. Consider dsinθ = cosθdθ (in radians). 2 Total Internal Reflection Generally, when light hits the interface, there is some reflection as well as refraction. If the light moves in the denser (higher n) medium toward the interface, then total internal reflection may occur. This happens if the angle of incidence is greater than the critical angle for the medium. At this angle, the angle of refraction is 90. If the outside medium is air, then Equation 1 gives sinθ c = 1 n (2) The cases of angle of incidence less than and greater than the critical angle are shown in Figure 2. Figure 2: Total internal reflection.
The apparatus setup is shown in Figure 3 Figure 3: Light refraction. 1. Place the ray box on a white sheet of paper on the table. Slide the ray mask until only one white ray is showing. 2. Position the rhombus as shown in Figure 3. Do not shine the ray through the rhombus too near the triangular tip. 3. Rotate the rhombus until the emerging ray just barely disappears. Just as it disappears, the ray separates into colors. The rhombus is correctly positioned if the red has just disappeared. 4. On the paper, mark the surfaces of the rhombus. Mark exactly the point on the surface where the ray is internally reflected. Also mark the entrance point of the incident ray, and the exit point of the reflected ray. Determine the critical angle. 5. Calculate the critical angle from Equation 2 and compare it with the measured value. 3 Focal Length of a Thin Lens For an image produced by a thin lens, 1 f = 1 d o + 1 d i (3) where f is the focal length, d i is the distance from the lens to the plane of the image, and d o is the distance from the lens to the object. These distances are shown in Figure 4
Figure 4: The setup for testing the thin lens equation. Thefocallengthisafixedpropertyofthelens; itisdeterminedbytheradiiofcurvature of the surfaces, and the lens index of refraction. If the object and image distances are different from those constrained by Equation 3, the image will be blurry. If the object distance is very large (d o ), then Equation 3 also predicts that the image distance is equal to the focal length. This is a convenient way of measuring the focal length of a positive (f > 0) lens. 1. On the optical bench, position the lens between a light source (the object) and a screen. 2. Move the lens to a position where an image of the object is formed on the screen. Measure the image distance and the object distance. 3. Repeat the above procedure for a least 3 additional, different object distances. Enter the data into Matlab. Plot 1/d o vs. 1/d i. Use the fit information to find the focal length. Compare this with the nominal value. 4. Estimate the focal length of the lens by measuring the image distance for a distant object (eg. a light at the other side of the room.) Compare this with the other values.
Figure 5: The various pieces of apparatus used in this experiment.