2. How could we perform part III of this experiment by measuring only distances? (There are multiple potential answers here; come up with a set of measurements you think are plausible to perform, physically speaking, and a formula relating them to your conclusion. Show your work.) Part III Quantity : Critical Angle Critical Angle sin(Crit. Angle) n(Glass) Does your measurement of n(Glass) agree with the expected value of n=1.5, to within uncertainty? : Yes Unit Degrees Radians Radians How does the intensity of the incident beam vary as you approach the critical angle? Same Value 42 0.7330 0.6691 1.494 How does the intensity of the refracted beam vary as you approach the critical angle? Dimmer Uncertainty 0.01 0.007431 0.02629 How does the intensity of the reflected beam vary as you approach the critical angle? Brighter Do your answers to the above three questions make sense together (given conservation of energy)? : YesIntroduction In this lab, we will investigate the basic principles of ray optics, emphasizing Snell's law and the Law of Reection. \"we" \"'9' these! Back to Top _ - Optics Kit: 0 Laser Apparatus o Triangular Prism 0 Rectangular Block o 20 Converging & Diverging Lenses 0 Plane Mirror 0 Graph Paper 0 Laminated Protractor Paper 0 Mini-ruler - Record data in this Google Sheets data table Back to Top Background Basic Principles of Reection and Refraction There are two phenomena that occur when a light beam hits an interface between two different kinds of material: refraction and reflection. 1 Refraction occurs when the light is transmitted into the new material, but at a different angle than it came in. Reflection occurs when the light reflects back into the material whence it came. In both cases, we first draw a line perpendicular to the interface, which we call the normal. The basic angles we deal with in optics are the angles between a beam of light and the normal, as seen below: Incident beam Normal 5 (perpendicular ' to surface) Material with index of refraction n1 Material with index of refraction n2 Refracted beam For reflections, the law ofreflection states that the incoming angle (with respect to the normal) and the outgoing angle (w.r.t. normal) are the same. This is true regardless of the details of the reflection (whether you are going "inside" a material to "outside," vice-versa, or bouncing off a mirror). For refractions, the angles are instead governed by Snell's law: 111 sin(91) : n2 sin(92) (1) Here, we label the two sides of the interface by 1 and 2 (with, usually, 1 being the side of the incoming beam, and 2 being the side of the refracted beam). The quantities 61 and 02 are then the angles (w.r.t. normal) of the light beam on the respective sides of the interface. The quantities in and n2 are the indices of refraction of the materials on each side of the interface. The index of refraction is a property ofa material which describes how fast light moves in a material (1;) vs. in vacuum (6): n: '1} Hence, 7:. = 1 for vacuum, and approximately so for air. Otherwise (generally), 71. > 1. 1 Total Internal Reflection When a beam of light moves from an area of higher 11 to lower n, depending on 61, it is possible that there is no 92 that will cause Snell's law to hold. In this case, no light can be refracted, and we have what is called total internal reection: all light is reflected back into the material (at an angle given by the Law of Reflection). This phenomenon happens if the incident angle (w.r.t. the normal) exceeds some critical angle 93. If the index of refraction in the region of the incident beam is 71.1 and on the other side of the material boundary is n2, then GC is determined by setting sin(32) equal to 1 in equation (1), producing the formula: sinw.) = (3) 711 Understanding Intensities You may wonder how much light is reflected and how much light is refracted, as a function of angle. Unfortunately, this is a surprisingly complicated question, and a full formula for the intensity of the reflected vs. refracted beams are beyond the scope of this course. Nevertheless, one basic principle that governs these powers can be understood. The intensity of the beam is the power (energy per unit time) transmitted per unit area. Therefore, by conservation of energy, if no light is absorbed (which is a separate possible phenomena), the total incoming intensity has to equal the total outgoing intensity (added over all outgoing beams). z Lens Basics Thus far, we have focused on reflection and refraction by flat surfaces. While the principles are the same for curved surfaces (just with a "normal" that varies over the surface of the material), the computations get more complicated to do "exactly." That said, most of the real use of optics comes from using curved surfaces to focus or defocus light, so it's important to work with. In general, we simplify by working primarily with arrangements of one particular kind of curved surface, a lens. 2 There are two kinds of lenses: converging (convex, focusing) lenses, which bulge "outwards," and diverging (concave, defocusing) lenses, which bend "inwards." We will be looking at both in this lab. Suppose a bunch of parallel light beams enter our lens. A converging lens has the outgoing light beams focus to a single point, known as the focal point. A diverging lens has the light beams bend apart, but in such a way that it appears they all come from a single point. The forward-displacement to the focal point is known as the focal length, f. (This means that if the focal point is behind the lens, as occurs for a diverging lens, then the focal length is negative.) An ideal lens (which makes this focal point exactly) is shaped like a (slice of a) parabola. However, far easier to manufacture is the spherical lens. Deviations from the "ideal" focal point clue to the lens being spherical is known as spherical aberration. An ideal lens also has an index of refraction which is independent of wavelength, so all colors focus in the same place. The breakdown of this assumption is known as chromatic aberration. Part III: Total Internal Reflection In this part, we will again measure angles; however, they will be determined with significantly less precision than the last part. 3 Place your triangular prism on the mini-protractor so that the hypotenuse is on the +90 line, so the right angle points towards 0. Shine the laser on the prism in the following way: Note: point where light is reflected must be center of protractor Refracted ray Just Protractor (small, barely disappears under prism) Rotate the laser until you reach the point where the outgoing refracted beam just disappears (by "folding into" the hypotenuse of the triangle). The angle on your protractor (if the laser is still pointed at the center of it!) is now the critical angle. Adjust your positions until you feel you've got the best measurement of critical angle you can get, and record that value. Estimate its uncertainty (however precise you think you were able to get). Now, let's make some qualitative observations of intensity. Rotate your prism so it's just outside the angle at which total internal reflection happens (so that you have a refracted beam that is almost gone). Now, wiggle it slightly. How do the incident, internally reflected, and refracted beams vary in intensity, if at all, as you approach the critical angle (from the direction where the refracted beam appears)? (This is most visible when you're really close to the critical angle.) Part IV: Parallel Rays Into Lenses Flick the lever on the laser box so that you get five light beams, and pull out both the converging ancl diverging lenses. Begin with the converging lens (the one that looks like a football). Shine the laser through it, and observe what you see. Then, place your setup on a sheet of paper, and trace both the light rays and the edge of your lens. Then, repeat with the diverging lens (the one that looks like someone took a brick and pinched the middle)