Lab 9 Refraction First, since the equipment we are using today is small, make sure that every person in your group gets a chance to see each individual experiment. Also, since much of our lab today is qualitative, be sure to include in your report sketches or diagrams of everything you observe, and answers to all questions. Finally, please use the handles on the lenses and mirrors instead of touching them directly. 1) Snell's Law Place the ray box on top of a piece of paper so that you will have a surface upon which to trace the rays. Project a single light ray upon the clear plastic, rectangular object so that the ray makes a large angle with the normal. Trace the object, the incident ray, and the ray that emerges from the opposite side. Then remove the object and use the straight edge to complete drawing the path of the refracted ray. Also, draw the normals at each plastic/air interface. Upon entering the plastic, does the ray bend toward or away from the normal? Upon leaving the plastic, does the ray bend toward or away from the normal? Snell's law states that for each plastic/air interface: nisino, = nasinez, where n, and na are the different indices of refraction for the two media and 0: and 02 are the respective angles each ray makes with the normal. Consider first the point where the ray enters the plastic. Carefully measure the two angles with respect to the normal. Then, using nor = 1.00 , solve for nplant. Repeat the process for the point where the ray leaves the plastic. Your two values for name should compare favorably. All lenses in your kit should have the same index of refraction, so you can use this value throughout the lab. Are the incident ray and the emergent ray parallel? Would this be true for all of the plastic shapes? (Try it.) For what shapes would this be true and why? Does a light ray bend when it is perpendicularly incident upon a surface? Explain mathematically why this is so. 2) Total Internal Reflection When a light ray is emerging from a medium of higher index of refraction into one of lower index of refraction, if the angle it makes with the normal is large enough, it will be totally internally reflected. This critical angle is given by Or = sin"(na/m:), where ni > na. Use the value for nplans that you just calculated to determine the critical angle for the plastic/air interface. Now we will determine this value experimentally. Aim a single beam of light at the shortest side of the 30"-60-90 prism, so that the refracted beam inside the prism strikes the hypotenuse as shown. Adjust the light box and prism positions until total internal reflection occurs and the ray emergesthrough the third side. Record the first position at which this occurs and measure the angle of incidence from the normal to the hypotenuse. This should be the same angle that you calculated a moment ago. Aim a single ray perpendicularly into the hypotenuse of the 45" prism at about a quarter of the distance from one end. This time the ray is totally reflected internally in the prism twice and returns on a path that is parallel to its original one but reversed in direction. Now aim three parallel rays into the 45' prism hypotenuse near one end. Sketch the path of each ray as it is doubly reflected. You may want to make them different colors to keep track of them. Are the ray positions reversed by the double reflections? Sketch the paths of the three rays If you were to use two such prisms in this way: Would the quadruple reflection (twice in each prism) restore the beams to their original relationship, or are they still reversed? Pairs of prisms arranged in such a manner are used in prismatic binoculars, to shorten the overall length of what would otherwise be a .5 m to .75 m long telescope. 3) Dispersion Have you noticed anything regarding the color of a light ray after it is refracted several times? Alm a single ray at the 60-60"-60" prism in this manner: Is the original beam white or colored? Is the emergent beam white or colored? Sketch the colors, and in which order they appear. For which color must the index of refraction in the plastic be the greatest? the least? 4) The Lens Maker's Equation The following formula indicates the relationship between refractive index, focal length and radius of curvature for a lens: 7= (0 -D) RI* R2 where R: and Ra are the radii of curvature of the two faces of the lens. Choose one of the converging lenses, (), from your kit. Measure the radius of curvature of both sides by tracing out an entire circle for each side. Now that you have found R; and Ra, and you know n for the plastic material, calculate the expected focal length, f, for the lens. Now test this result by projecting parallel rays on the lens, tracing the lens and rays, and measuring the distance from the center of the lens to the focus, f. Your values should compare within the range of uncertainty. Repeat this procedure for the other converging lens. Repeat this procedure for the diverging, )(, lens. This time you will need to extend the rays behind the lens to find the focus.5) n W w wi h h R x ". Just as we found in studying mirrors, the path of a light -. ray can be traced without actually projecting a beam of \\ light. We can use a sighting line instead. Trace the outline of the rectangular object on a piece of paper with cardboard underneath. Place two object pins so that they describe the path of a ray of light entering the object as shown. Look through the object from the opposite side and use a straight edge as a guide to draw the path of the emerging ray (the sighting line for which one pin appears to line up directly behind the other). Remove the object and use the straight edge to complete drawing the path of the ray through the object by connecting the entering and emerging points. Now demonstrate that a ray from the light box follows the exact same path that you picked out by sight