Chapter 4 Experiment 2: Snell’s Law of Refraction 4.1 Introduction In this and the following lab the light is viewed as a ray. A ray is a line that has an origin but does not have an end. Light is an electromagnetic disturbance and, as such, is described using Maxwell’s equations, which expresses the relationship between the electric and magnetic fields in an oscillating wave. Light propagates as a wave; yet, many optical phenomena can be explained by describing light in terms of rays. In the model for light, rays in a homogeneous medium travel in straight lines. This model is referred to as Geometric Optics and is a very elementary theory. In this theory light travels from its origin at a source in a straight line, unless it encounters a boundary to the medium. Beyond this boundary may be another medium which is distinguished by having a speed of light different from the original medium. In addition, light may be reflected at the boundary back into the original medium. A light ray that returns to the original medium is said to be “reflected”. A ray that passes into the other medium is said to be “refracted”. In most interactions between light and a boundary, both reflection and refraction occur. In order to frame laws that govern these phenomena we must define some terms. The boundary between two media is defined as a surface. The orientation of a surface at any specific point is characterized by a line perpendicular to the surface that we call the normal. A ray may encounter a boundary at any arbitrary incidence angle. The angle of incidence is measured with respect to the normal line. A reflected ray will have an angle of reflection that is also measured with respect to the normal. The refracted ray will be oriented by the angle of refraction measured between the ray and the normal to the surface. Checkpoint For geometric Optics what assumption is made about the nature of light? 39 CHAPTER 4: EXPERIMENT 2 What distinguishes the two media is that the speed of light is different from one medium to the other. We define the index of refraction n to be the measure of how much different the speed of light is in a certain medium from that of light through a vacuum. Light travels through a vacuum at 299,792,458 m/s. This speed is thought to be a universal constant and the highest speed allowed in nature as postulated in Einstein’s theory of Special Relativity. We use the symbol c to represent this speed. The index of refraction is a characteristic of the medium. It is the only thing that distinguishes one medium from another in geometric optics. It is defined as the ratio of the speed of light in a vacuum to the speed in a particular medium of interest, c c n = or v = . (4.1) v n Therefore, the value of the index of refraction is always greater than unity. Gasses have an index of refraction close to 1 (nair = 1.00028), while for water the index is about 1.33 and for plastic it is approximately 1.4. Depending on the type of glass the index of refraction of glass can vary from 1.5 to 1.7. Normally we might think that the index of refraction is a constant that is the same for all light. The index of refraction actually depends on the frequency (color) of the light wave to a small degree across the visible part of the spectrum and as such is different for different colors of light. The rules for reflection of light are: 1) The angle of incidence is equal to the angle of reflection, 0 θ1 = θ1 (4.2) 0 where θ1 is the angle of incidence and θ1 is the angle of the reflected ray that propagates in the same medium. (This is the commonly known rule, but this next rule is rarely stated though equally important) 2) The incident ray, the reflected ray, and the normal to the surface, all lie in the same plane. Checkpoint What is the law of reflection? We will not formally investigate these rules in this lab although you will be able to observe the phenomena of reflection as a side issue while performing this lab experiment. The rules for refraction are not so obvious although they where well known to the ancients. 1) The first rule is often cited as Snell’s Law; it is: sin θ1 n2 = or n1 sin θ1 = n2 sin θ2. (4.3) sin θ2 n1 40 CHAPTER 4: EXPERIMENT 2 where θ2 is the angle of refraction of the ray that is transmitted into the second medium. 2) The incident ray, the refracted ray and the normal to the surface, all lie in the same plane. Checkpoint What is Snell’s Law? What phenomenon does Snell’s Law describe? In general the path of a light ray is reversible in that if a light ray were to be reversed it would follow the same path. A ray traveling from a low index of refraction to a high index of refraction will experience a bending toward the normal. However a ray passing from a high index of refraction to a lower index will experience a bending away from the normal. The angle of refraction will be larger than the angle of incidence. So, what happens when the angle of refraction is greater than 90◦ for a given incidence angle. In this case light cannot be transmitted through the interface and as such it is reflected totally. The efficiency for this reflection is 99.99% (as compared to 95% for a typical silvered surface mirror). The largest angle for which a ray will be transmitted is the critical angle. One can show that the sine of this angle is the inverse of the ratio of the index of refraction of the first medium to the index of the second medium. If the second medium is air (n = 1.00028), the sine of the angle is effectively the reciprocal of the index of refraction of the first material. Checkpoint In optics angles are always measured with respect to what? 4.2 The Experiment The experiment consists of a single thin bundle of light rays exiting a light box. This ray will be incident upon a ‘D’ shaped dielectric so that we may deduce whether the laws of reflection and of refraction are obeyed by the interaction between the light and the object. A picture of the experiment is shown in Figure 4.1. We should recall that ‘dielectrics’ were placed between capacitor plates to increase capacitance and to insulate between the plates. Our refracting medium is a transparent dielectric. 4.2.1 Reflections and Refraction In this experiment you will use the Light Ray Box shown on the right side of Figure 4.1. It consists of a light source and a Multi-slit Slide Set. The light source housing is mounted on 41 CHAPTER 4: EXPERIMENT 2 a colored plastic base in which it can slide back and forth. The utility of this feature will be explained in a future experiment. The Multi-slit Slide is a flat square piece of plastic or aluminum with notches cut into each of the four edges. The Multi-slit Slide slips into a slot on the end of the ray box to create rays of light. Choose the side with just one narrow notch and place that side down as you slip the a Multi-slit Slide into place. A single narrow beam should be observed emerging from the ray box. Also in this experiment you will use a turntable (goniometer) to orient the dielectric surface. The turntable has some friction with its stationary stand, so it is suggested that you spend several minutes practicing the act of changing angles before aligning the experiment to take your data. With some care you should be able to rotate the turntable and dielectric on its stand without sliding the stand on the tabletop. Once you can do this reliably, carefully place the dielectric ‘D’ on the turntable as the turntable markings indicate. As long as you do not suddenly move the turntable, friction will keep the dielectric on the turntable at this location and will allow you to rotate the dielectric while reading the angles from the turntable’s periphery. Figure 4.1 shows the experiment in progress. In the figure the light passes through the dielectric before striking the planar surface (the ‘relevant surface’ in the figure). Note that the ray strikes the planar surface precisely at the center of the turntable; this is also the pivot point for the turntable. As long as neither the ray box nor the turntable slides on the tabletop, this ray will always strike the relevant surface at the pivot point. In the figure it is easy to see that the incident ray is 40◦ from one side of the normal and the reflected ray is 40◦ from the opposite side of the same normal. The refracted ray has spread considerably (can you guess why?), but its refraction angle is about 73◦ (what is its uncertainty?). Is there any trend that you note regarding these refracted rays and how they spread? 4.2.2 Index of Refraction and the Law of Reflection Now we need to align the ray from the ray box carefully before we begin taking data. Carefully rotate the turntable so that the flat side of the dielectric faces the ray box.