Relection and Reraction Object To determine ocal lengths o lenses and mirrors and to determine the index o reraction o glass. Apparatus Lenses, optical bench, mirrors, light source, screen, plastic or glass disk. 3 Theory 3. Relection and Reraction For relection, the angle o incidence i should equal the angle o relection r as shown in igure. When a light ray is transmitted rom one material into another the process is called reraction. i r Figure : Relection o o a smooth, lat surace oten termed specular relection. It is customary to measure all angles with respect to the normal, which is perpendicular to the interace between the media at the point o incidence. Snell s law describes what happens at such an interace n sinθ = n sin θ () where n and n are the indices o reraction o the two materials, θ is the incident angle, and θ is the reracted angle. The index o reraction is deined as the ratio o the speed o light in vacuum (space) over the speed o light in the material in question. Mathematically, n c/v. For air, n, and or water n =.33, whereas oten n =.5 or glass. It has also been ound that n will vary as a unction o wavelength (or color) o light. Thus, white light entering a second material will have its dierent colors reracted at dierent angles and oten the separate colors will become observable. A geometrical derivation or Snell s Law can be ound in most Physics texts. In general when light hits the interace between two dierent media, some o the light will be relected and some will be reracted, with each obeying the above laws, accordingly. This is shown in igure. The amount relected versus reracted depends on several variables, including the indices o reraction and the incident angle.
θ θ n n θ Figure : Reraction (and relection) at the interace o two dierent media. The relected ray obeys the Law o Relection, and the reracted ray obeys Snell s Law. In Snell s law, i n > n, then the reracted ray will bend away rom the normal, meaning that θ > θ. As θ is increased, θ also increases, until θ = 90. Under these conditions no light is reracted into the second material and the angle θ is reerred to as the critical angle o incidence or total internal relection. 3. Lenses By applying the laws o relection and reraction to mirrors and lenses, respectively, one arrives at the ollowing expression: = p + () q where p is the distance rom the mirror/lens to the object (object distance) and q is the distance rom the mirror/lens to the image (image distance); means the ocal length o the mirror/lens in use. The ocal length is deined as the point at which all parallel rays o light meet ater relecting o o the mirror or passing through the lens. For diverging mirrors/lenses, it is the point rom which the diverging rays appear to come. This is shown or lenses in igure 3. Figure 3: Parallel rays incident on a convex (converging) lens (top) and onto a concave (diverging) lens (bottom). The ocal lengths are labelled.
When multiple lenses are used, one treats one lens at a time. Equation is applied to the irst lens using its ocal length to ind the image distance q, given a known object distance p. This image then becomes the object or the second lens, where one needs to igure out the object distance p and then use it with the ocal length o lens # ( ) to ind the inal image distance q. This process repeats or as many lenses as are in the array. 4 Procedure 4. Lenses. Using the optical bench allow light rom a distant light source (p ) to all on a converging lens. Move the lens until a clear image is ormed on the screen. The screen should be on the opposite side o the lens rom the light source. Record the distance rom the lens to the screen q. Repeat this or the two other converging lenses, and record the ocal lengths or later use.. Using a small light source (arrows), move the lens until the image o the light source is clearly ocused on the screen. Record the distance rom the light source to the lens (p) and the distance rom the lens to the screen (q). Repeat this or three dierent object distances. 3. Repeat the above step or the other two lenses rom the irst part. 4. Using the same light source as above, place two lenses between the light and the screen. Adjust the placement o these lenses until a clear image orms on the screen. Record the distance rom the light source to the irst lens (p ), the distance rom the second lens to the screen (q ), and the distance between the two lenses (D). Repeat this process our times or other lens combinations. Use the diverging lens in one combination, but only as the second lens. 5. Using any two lenses, adjust the distances until the magniication is two. Record the same inormation as earlier in this procedure section on your data sheet. 4. Mirrors and lenses. Position the concave mirror symmetrically to the axis as shown in igure 4 and have the central ray o the light source along the axis. Draw the incoming parallel rays and the relected rays, as well as the relection surace o the mirror. Using your sketch, ind the ocal length o the mirror. parallel rays o light concave mirror optic axis Figure 4: Parallel rays incident on a concave mirror. 3
. Repeat or a convex mirror, and be sure to extend the rays back to ind the ocus. 3. Repeat the same procedure or the convex and concave plastic lenses. 4. Place the semicircular glass plate rosted ace down on the polar graph paper so that the middle o the straight edge o the plate is at the center o the paper with the straight edge along the 90 90 line. Project a single ray into the middle o the straight edge o the plate (center o the paper) so that the angle o incidence in air is 0. Record the angle o reraction. Repeat or angles o 0, 30, 40, 50, and 60 degrees. Record angles o reraction to the nearest 0.5. 5. Project a light ray into the circular surace o the glass plate so that it is normal to the circular surace and emerges rom the straight surace into air at the center. The angle o incidence is now in the glass, and the angle o reraction is in air. Start with a small angle o Figure 5: A light ray incident normally on a glass semi-circle showing the relected and reracted rays. incidence and rotate the incident ray to larger angles, keeping the ray incident at the center o the straight edge o the glass s straight edge. When the reracted ray becomes 90, then the incident angle is the critical angle record it. Rotate the incident ray urther and note what happens. 5 Calculations 5. Lenses. Determine the ocal length o each lens using equation. Using a percent error, compare your values to those on the lenses.. Using equation calculate the ocal length o each lens. This is done our times or each lens. Calculate a mean and error or each lens and compare to the given value. 3. Calculate the ocal length o the second lens in the combination. Use the given value or the ocal length o lens #, and compare your results that obtained above. As mentioned above, you must use equation twice, once or each lens, to arrive at your answer. For the data or the last measurement (magniication o ), check the validity o the expression or the magniication o a lens m = q (3) p 4
For two lenses the total magniication is the product o the individual magniications o the two lenses: m T = m m (4) A negative magniication means that the image is inverted with respect to the object. 4. For the semi-circular glass, calculate the index o reraction o it using equation. Calculate a mean and error or these values o n. 5. From your critical angle data or total internal relection, calculate the index o reraction o the glass again using equation. Compare this value to that just obtained above. 6 Questions. For your magniication o lenses, sketch a ray diagram to scale and label all distances clearly.. Is the magniication o a converging lens always less than? Explain. 3. Explain how optical ibers use total internal relection. 5