Materials: PHET Simulation “Bending Light” at https://phet.colorado.edu/en/simulation/bending-light Part A Procedure 1. Open the simulation “Bending Light” at PhET. 2. Click on Intro. 3. Leave the default for entry material at “Air”. Choose “Glass” for the exit material. Record the index of refraction of glass here 4. Choose the protractor and set the laser to an angle of incidence, ? 1, at 30 0 . Note that angles are always measured from the Normal (dashed line, perpendicular to the surfaces) 5. Ignore the reflected ray (the ray that remains in air). Using the protracr, measure the angle of refraction, ? 2 , of the laser and record in Table 1. 6. Repeat steps 4 and 5 of this lab for the given angles of incidence. Record the results in Table 1. Data: Table 1 Trial n 1 (air) ? 1 (degrees) ? 2 (degrees) Sin ? 1 Sin ? 2 n 2 1 2 3 4 5 Part B Procedure 1. Reset simulation and choose “Mystery B for the bottom medium. 2. Choose the protractor and set the laser to an angle of incidence, ? 1 at 30 0 3. Ignore the reflected ray (the ray that remains in air). Using the protractor, measure the angle of refraction, ? 2 , of the laser and record in Table 2. 4. Repeat steps 2 and 3 for the remaining trials using the given incident angles. Record the results in Table 2. 5. Calculate sin ? 1 and sin ? 2 for each trial. Record the results in Table 2 Table 2 Trial ? 1 (degrees) ? 2 (degrees) Sin ? 1 Sin ? 2 1 2 3 4 5 1. Draw a graph of the Sin ? 2 vs. Sin ? 1 on the grid below. Draw in your best-fit line and find the slope. Show slope work below. 2. Using the slope, you calculate above and the chart below, identify the mystery material in your experiment. Media Index of Refraction Vacuum 1.00 Air 1.0003 Carbon dioxide gas 1.0005 Ice 1.31 Pure water 1.33 Ethyl alcohol 1.36 Quartz 1.46 Vegetable Oil 1.47 Olive oil 1.48 Acrylic 1.49 Table salt 1.51 Glass 1.52 Sapphire 1.77 Zircon 1.92 Cubic zirconia 2.16 Diamond 2.42 Gallium phosphide 3.50 3. Find the percent error of your observed value (from the slope) using the identified index of refraction as your value %Error = | measured – accepted / accepted | x100 Analysis Questions: 1. Substitute the average value of the index of refraction that you measured in Part A into the equation for index of refraction and calculate the speed of light in the glass. Show work. 2. What if you conducted this experiment (Part A) under water? Compare and contrast the results you get in such a situation to the results you have from this lab.
The Correct Answer and Explanation is :
Part A Answer and Explanation:
- Index of Refraction of Glass (n₂):
- From the simulation, the index of refraction for glass is approximately 1.52. This is a standard value that can be found in many tables of materials’ optical properties.
- Table 1 will include values for θ1\theta_1 (angle of incidence), θ2\theta_2 (angle of refraction), and the values for sin(θ1)\sin(\theta_1), sin(θ2)\sin(\theta_2), and other variables.
- The experiment measures the relationship between the angle of incidence and the angle of refraction when the light passes from air (with a refractive index of approximately 1.00) into glass (refractive index approximately 1.52). The angles of incidence and refraction obey Snell’s Law: n1⋅sin(θ1)=n2⋅sin(θ2)n_1 \cdot \sin(\theta_1) = n_2 \cdot \sin(\theta_2) where:
- n1n_1 is the refractive index of air (1.00),
- n2n_2 is the refractive index of the second material (glass, 1.52),
- θ1\theta_1 is the angle of incidence,
- θ2\theta_2 is the angle of refraction.
- Snell’s Law Analysis: For each trial, as the angle of incidence increases, the angle of refraction also increases, but at a slower rate due to the higher refractive index of glass compared to air. This is consistent with the bending of light when passing from a less dense medium (air) to a denser medium (glass).
- Graphing and Slope Calculation: After plotting sin(θ2)\sin(\theta_2) vs. sin(θ1)\sin(\theta_1), the slope of the best-fit line will give us the ratio of refractive indices. From Snell’s Law, we can express the relationship: sin(θ1)sin(θ2)=n2n1\frac{\sin(\theta_1)}{\sin(\theta_2)} = \frac{n_2}{n_1} Using the slope of the graph, we can calculate the index of refraction of the mystery material (in Part B).
- Percent Error Calculation: The percent error can be found using the formula: %Error=∣measured value−accepted valueaccepted value∣×100\%Error = \left| \frac{\text{measured value} – \text{accepted value}}{\text{accepted value}} \right| \times 100 In this case, the accepted value of the refractive index for glass is 1.52. If the slope from the graph differs slightly, the error could be due to experimental limitations such as precision in angle measurement or slight deviations in the simulation.
Part B and Further Analysis:
- Using Mystery Material: After completing Part A, you’ll identify the refractive index of the mystery material based on your graph’s slope. The material whose refractive index is closest to the value derived from your experiment is likely the mystery material.
- Comparing Results for Underwater Experiment: If this experiment were conducted underwater, the refractive index of water would need to be considered. Water has a refractive index of approximately 1.33, which is slightly higher than air but lower than glass. The change in the speed of light in the water would affect the angle of refraction, making it less pronounced than in air. The light would bend more toward the normal in water than in air, but less than in glass. This demonstrates how the surrounding medium’s refractive index impacts the light’s behavior. Underwater, the refractive indices of both water and glass would influence how light bends as it passes from one material to another, compared to air, where the light bends more dramatically due to the larger contrast in refractive indices.
Conclusion:
This experiment demonstrates the principles of light bending (refraction) as it passes through different materials with varying refractive indices. By measuring and calculating angles and using Snell’s Law, we can better understand the relationship between light and the medium it travels through.