Student Exploration: Basic Prism

Name: Ariel Villaroel Date: 20/10/2024 Student Exploration: Basic Prism Vocabulary: angle of incidence, angle of refraction, critical angle, dispersion, index of refraction, medium, prism, refract, Snell’s law, total internal reflection, visible spectrum, wavelength Prior Knowledge Questions (Do these BEFORE using the Gizmo.) A prism is a transparent object that can be used to bend, or refract, light. The photo below shows what happens when sunlight passes through a prism. W hat do you see ? White light being tra nsformed to a rainbow . What does this indicate about the composition of sunlight? Gizmo Warm-up The Basic Prism Gizmo allows you to investigate how a prism refracts light. The Gizmo shows a laser emitting a beam of light through a triangular prism. To begin, check that Single color beam is selected, ? is 500 nm, n is 1.50, w is 2.0, and the angle (?) is 0°. What do you notice about the path of light when it passes through the prism? It bends downwards or refracts. M ove the ? slider to increase and then to decrease the wavelength of the beam of light. How does this affect the color of the light ray? As the wavelength increases the color changes to warmer colors (orange, red, yellow) and to colder colors when the wavelength decreases. How does this affect the direction of the light ray? As the wavelength increases the direction of the light raises and the opposite happens when the wavelength decreases. Get the Gizmo ready: Set ? to 500 nm and n Activity A: to 1.00. Check that Refraction and dispersion w is 2.0 and ? is 0°. Introduction: When light passes from a vacuum into a medium such as glass, it slows down. The index of refraction (n) is equal to the ratio of the speed of light in a vacuum to the speed of light in a medium. The index of refraction of air is very close to 1.00. Question: What factors affect the refraction of light through a prism? Observe : What do you notice about the beam of light when the n is 1.00? The light point straight and does not bend. Predict : How do you think increasing the index of refraction will change the path of the l ight? Observe : Slowly increase n to 1.50 , close to the value for glass. What happens ? The light begins to bend downward. Observe : Increase n to 1.53. What happens now? The light no longer leaves the prism but bends backwards. Gather data : Set n to 1.50. The Gizmo also allows you to change the width of the prism ( w ), the angle of the prism ( ? ), and the wavelength of the light ( ? ). Describe the effect of each action listed below . Return the Gizmo to its starting conditions after each trial . Action Effect on path of light ray exiting the prism Decrease w to 1.0. The prism appears more narrow altering the angle of refraction Increase w to 3.0. The prism widens, the beam of light now has three refractive rays Decrease ? to -30°. The prism has turned, changing the angle of the refractive angles Increase ? to 30°. The prism is tilted however the first entry of the beam into the prism is not refracted Decrease ? to 400 nm. The light beam is now purple Increase ? to 700 nm. The light beam is now red (Activity A continued on next page) Activity A (continued from previous page) Summarize : Which actions caused the amount of refraction to increase? Increasing the width of the prism. Think and discuss : Why does widening the prism cause the beam to bend more? If possible, discuss your answer with your classmates and teacher. Observe : Return the Gizmo to its initial settings ( n = 1.50, w = 2.0, ? = 0°). Select White light from the menu at upper left. What happens when white light goes through a prism? Explain : Why is a spectrum of colours produced when white light passes through a prism? (Hint: Think about the effect of the wavelength of light on how much it refracts .) Get the Gizmo ready: Select the Single color beam . Check that ? is 500 nm , Activity B: n is 1.50, Snell’s law w is 2.0 , and ? is 0°. Turn on Show protractor . Introduction: When light crosses a boundary from one medium into another, there are several important angles to keep in mind. One is the angle of incidence (?i), which is the angle between the beam of light and the normal to the boundary. (A normal is an imaginary line that is perpendicular to the boundary.) The other is the angle of refraction (?r), which is the angle between the refracted beam of light and the normal. Question: How can the angle of refraction be determined? Measure : To measure the angle of incidence, do the following: Drag the center of the protractor (the gray circle) to the junction of the light ray and the prism, as shown. The red line is the normal. Rotate the red line so that it is perpendicular to the edge of the prism. (The gray line should be aligned to the edge of the prism .) Rotate the green line so that it aligns to the light beam. Measure : To measure the angle of refraction, rotate the green line so that it lines up with the light beam inside the prism. Gather data : The index of refraction of air ( n 1 ) is 1.00, and the index of refraction of the prism ( n 2 ) can vary. For each value of n 2 in the table below, find ? i and ? r . n1 n2 ?i ?r sine(?i) sine(?r) n1 · sine(?i) n2 · sine(?r) 1.00 1.50 28 19 0.5 0.33 0.5 0.48 1.00 1.75 28 16 0.5 0.28 0.5 0.48 1.00 2.00 28 14 0.5 0.24 0.5 0.48 Calculate : Use a scientific calculator to find the sine of each angle . Then find the product of the sine of each angle and its associated index of refraction to complete the table. (Activity B continued on next page) Activity B (continued from previous page) Analyze : What do you notice about n 1 · sine( ? i ) and n 2 · sine( ? r )? All the n1 · sine( ? i ) values stayed the same and n2 · sine( ?r ) values decreased when the index of refraction of the prism was altered . Manipulate : This relationship is called Snell’s law : Practice : What will the angle of refraction be for a beam of light moving from air into a prism if the angle of incidence is 80° and the prism’s index of refraction is 1.75? ?r = 34.2 degrees Practice : Snell’s law also applies to situations where the beam of light is moving from the prism in to air. In this case , n 1 is the index of refraction of the prism and n 2 is the index of refraction of air, or 1.00. ?r = 53.1 degrees Challenge : The critical angle is the angle at which total internal reflection occurs. This happens when the angle of refraction exceeds its maximum possible value of 90°. Rearrange Snell’s law to solve for the critical angle. (Hint: Set ? r to 90° and solve for ? i . ) Apply : Find the critical angle for a prism with an index of refraction of 1.50. Check your answer using the Gizmo. ?i = 41 degrees