Investigation 19 - Reflection and Refraction(3)

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Feb 20, 2024

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Investigation 19 – Reflection and Refraction Introduction Geometric optics is the study of light while using the ray model. In the ray model, light moves in a straight line unless it interacts with another material (i.e., a mirror, lens, etc.). Reflection is when a light ray bounces off of a shiny surface. This process is what allows a person to see themselves in the mirror. When light is reflecting, we define the angle of incidence (θ i ) as the angle from the normal to the surface at which the light is striking the reflective surface and similarly the reflected angle (θ rl ) as the angle the reflected light leaves the surface at with respect to the normal. These angles are defined in the picture below. Refraction is the bending of light as is moves from one medium to another. When a straw is in a glass of water it looks bent or even broken to an observer. This happens because of the light refracting as it transitions from the air to the water in the glass. When light transmits from one medium to another it bends (i.e., changes direction of travel) due to differences in how materials interact with light. We can quantify the interaction between materials and light with a material property called the index of refraction. The index of refraction for a material describes how well and how quickly the material allows light to propagate through it. When light is refracting, there is a relationship between the refracted angle (θ rr ) and the incident angle (θ i ) called Snell’s Law shown below: where n 1 is the index of refraction for the first medium, n 2 is the index of refraction for the second medium, θ i is the incident angle, and θrr is the refracted angle. These angles are defined in the picture below.

Activity 1 – Reflection and Refraction 1. Design an experiment with the rest of the class to test the relationship between the incident angle (θi), the reflected angle (θrl), and the refracted angle (θ rr ). (Make sure your experiment design includes the measurement of each light ray!) 2. Have your instructor run the experiment you designed. 3. Record the measurements in Table 1 below. Table 1 Incident Angle (Degrees) Reflected Angle (Degrees) Refracted Angle (Degrees) 0° 5° 10° 15° 20° 25° 30° 35° 40° Activity 2 – Refraction 1. What is the mathematical relationship between the incident angle (θ i ) and the reflected angle (θ rl ) you can determine from your data? 2. Does the incident angle equal the refracted angle? 3. In Table 2, the sine of the incident angles from Table 1 have been calculated and reported. Copy the refracted angles from Table 1 to Table 2. 4. Calculate the sine of the refracted angle for each angle. Record these angles in Table 2. 5. Calculate the ratio of the sine of the refracted angle over the sine of the incident angle. Record these values in Table 2 below.

Table 2 Incident Angle Sin(θi) (degrees) Refracted Angle Sin(θrr) (degrees) Sin(θi)/Sin(θrr) 0° 0.000 5° 0.087 10° 0.174 15° 0.259 20° 0.342 25° 0.423 30° 0.500 35° 0.574 40° 0.643 6. Does your data support Snell’s law? Why or why not? 7. The refraction we observed happens at the back surface of the object. Therefore, n 1 is for air and n 2 is for acrylic. What is the index of refraction of the acrylic (n 2 )? Take n 1 = 1 for air. 8. These lenses are made of acrylic which has an index of refraction of approximately 1.49. Calculate the percent difference between this theoretical index of refraction and the index of refraction you calculated. 9. What could have caused the theoretical and experimental indices of refraction to differ?

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