The Refraction of Light (Prepared by J. V. as Honor component, Spring 2020) Lab Goals To determine how light is refracted when different materials are used, to find the index of refraction for two unknown substances, to explore the concept of total internal reflection, and to find the critical angle of a substance. Theory Light travels with different speeds through different materials. This speed depends on how quickly photons will be absorbed and subsequently reemitted by a certain substance. The ratio of the speed of light in a vacuum to the speed of light in a substance is called the index of refraction, and is given by the following formula: n = The Index of Refraction where c is the speed of light in a vacuum and v is the speed of light in a material. When a beam of light passes from one material (or a vacuum) to a different material with a different index of refraction at an angle, the beam will be bent. By convention, the angle of the incident ray of light, or the incoming ray, and the refracted ray are measured according to the normal line, which is perpendicular to the boundary between the two materials. If a beam of light moves from a material with a Normal higher index of refraction to a material with a lower index, the angle Refracted of refraction will be greater than the angle of incidence, as indicated ray in the figure below. Conversely, moving from a material with a 82 lower index to one with a higher index will cause the refracted beam Air (n2) Water (n) to have a smaller angle. Reflected ray Incident ray SourceThe angle of incidence and the angle of refraction are related to the index of the refraction by Snell's law. This law is stated as: n1 sin01 = n2 sin02 Snell's law where n, and 01 are, respectively, the index of refraction and the angle of incidence in the original material; and n2 and 02 are, respectively, the index of refraction and the angle of refraction in the new material. Not all the light in a beam will be refracted: some of the photons will be reflected at the boundary between the two materials, as shown in the figure on the previous page. As stated earlier, when light moves from a material with a higher index of refraction to a material with a lower index, the ray will be refracted away from the normal line. At a certain point, when the angle of incidence is far enough from the normal line, the angle of refraction will be exactly 90%. After this point, increasing the angle of incidence will cause the exiting ray to be completely reflected instead of refracted, and the reflected ray will follow the law of reflection (the angle of incidence will equal the angle of reflection). This phenomenon is called total internal reflection. The angle of incidence which causes the angle of refraction to be 90 is the angle at which total internal reflection begins and is called the critical angle. By rearranging Snell's law, the critical angle can be found by the given formula: sin O c = The Critical Angle where 0 is the critical angle, and n, and ny are the index of refraction of the material where the light beam originates and the index of refraction of the second material, respectively. Procedure O Wave All of the activities in this lab will use Material A the following PhET simulation by the University of Colorado Boulder: Bending Light ndux of Flufunction in 1.33 Once the link is opened, click on the "Intro" simulation Normal Bending Light PHET. = 2Activity A: Finding the Index of Refraction 1) Set the upper material as water and the lower material as "Mystery A." 2) Turn on the laser and use the included protractor to measure the angle of incidence and the angle of refraction. 3) Set the angle of incidence to be the following angles and measure the resulting angle of refraction. 4) Use Snell's law to find the index of refraction at each angle and average your findings to find the index of refraction of the mystery material. Angle of Incidence Angle of Refraction Index of Refraction 100 300 450 60 80 Calculated Average Index of Refraction (n2): Question: Why cannot the index of refraction of any material be less than 1? Activity B: Total Internal Reflection 1) Set the upper material as "Mystery A" and the bottom material as "Mystery B." 2) Using the same steps as in the previous activity, find the index of refraction of the material "Mystery B." Angle of Incidence Angle of Refraction Index of Refraction 100 200 300 Calculated Average Index of Refraction:3) Using the index of refraction that you found in Step 2, calculate the critical angle for this setup. 4) Experimentally find the critical angle by moving the laser until the angle of refraction is exactly 90 Calculated Critical Angle Experimental Critical Angle Question 1: Did your experimental critical angle match your calculated critical angle? Question 2: Based upon what you learned in Activity B and the fact that mirrors do not reflect 100% of the incoming light, explain what great advantage comes from utilizing total internal reflection instead of mirrors. Give an example of one such application