Spotting a rainbow can really brighten a rainy day. A rainbow forms when sunlight shines on raindrops. Under the right conditions, the raindrops act like tiny prisms. White sunlight enters the raindrops. Before the light exits the raindrops, it spreads out into many colors. When you look up into the sky, you see these colors in the form of a rainbow. You can learn more about rainbows by experimenting with a prism.

Prism Basics

In this activity, you will observe what happens when light enters and exits a prism.

  1. In the Gizmo™, verify that n (index of refraction of the prism) is set to 1.50, w (width of prism) is set to 2.0, and θ (angle of prism) is set to 0°. Be sure that Single color beam is selected and that λ (wavelength of light) is set to 500 nm.
    1. What happens to the path of the light as it enters the prism?
    2. What happens as the light exits the prism?
    3. Does the light continue bending as it travels through the prism, or only at the points of entry and exit? Make a sketch to show this.
  2. Refraction is the bending of light. Light refracts when its speed changes as it travels from one medium into another. The index of refraction (abbreviated n) of a medium is a measure of how much that medium slows down or speeds up light.
    1. Use the slider to decrease n (the index of refraction of the prism) slowly from 1.50 to 1.00. How does decreasing n affect how the light refracts?
    2. The index of refraction for air is very close to 1.00 (actually about 1.0003). Describe the path of the light when the prism's n value is set to 1.00. Why does this make sense?
    3. Now slowly increase n from 1.00 to 2.00. What happens as n increases from 1.00 to 1.50? What happens for values of n > 1.50?
  3. The index of refraction of the prism is not the only thing that affects how much light refracts. To explore other factors, first set n back to 1.50. (To set a slider to a specific value, type the number in the field next to the slider and hit Enter.)
    1. Set θ to 30°. How much does the light refract when entering the prism? Why do you think this is so?
    2. Set θ to –50°. In this case, does light refract more entering or exiting the prism? Explain why.
    3. Set θ back to 0°. Then decrease the prism width (w) slowly from 2.0 to 1.0. How does this affect the amount of refraction?
    4. Is the amount of refraction affected by how far the light has to travel inside the prism? To test this, drag the laser up and down. What do you observe?
    5. Based on what you have seen, explain why light refracts less through a narrower prism.
  4. Set the Gizmo back to its original settings: n = 1.50, w = 2.0, and θ = 0°. Be sure that Single color beam is still selected, with the light wavelength set to λ = 500 nm. Now vary the wavelength (color) of light using the λ slider.
    1. Which color of light is refracted more, violet (λ = 400 nm) or red (λ = 700 nm)?
    2. In general, state how the wavelength of light is related to the amount that it refracts.
    3. White light contains all colors of visible light. Select White light from the dropdown list. What does the prism do to white light? Explain why this happens, based on what you have seen the prism do to single-color beams.
  5. The separation of white light into its component wavelengths is called dispersion. (Note: In the real world, the spectrum of white light is continuous. For simplicity, the Gizmo shows it as many individual beams.) Dispersion happens because the index of refraction of a prism is different for different wavelengths. In the Gizmo, the value of n shown is the prism's index of refraction for λ = 500 nm.
    1. If n is set to 1.50 in the Gizmo, is the value of n for λ < 500 nm greater than or less than 1.50? What about for λ > 500 nm? Explain.
    2. There is one value of n that does not cause dispersion of white light. For this value of n, the index of refraction of the prism is the same for all wavelengths of light. What is this value? Use the Gizmo to test your answer.

Critical Angles and Snell's Law

In this activity you will explore a few characteristic angles related to light and prisms.

  1. When light travels from one medium to another, the amount of refraction can be measured by comparing two angles: the angle of incidence and the angle of refraction. Both are measured relative to a normal line, which is perpendicular to the side of the prism. This is shown below.

    prism diagram
    1. When light exits a prism and refracts, as shown, which is larger, the angle of incidence or the angle of refraction? Explain.
    2. If no refraction occurred, how would the angle of incidence and the angle of refraction compare? (You can try this in the Gizmo by using n = 1.00.)
    3. What is the largest possible value for the angle of refraction? Explain.
  2. The image above uses the original settings of the Gizmo (n = 1.50, w = 2.0, and θ = 0°, with Single color beam and λ = 500 nm). Set the Gizmo up in this way, and then click on Show/hide protractor to show the Gizmo's angle tool. Measure the angle of incidence and the angle of refraction by following these steps:
    • Drag the vertex of the angle tool onto the point where the light beam exits the prism.
    • Rotate the small red circle counterclockwise until the gray line sits on the right edge of the prism. (This makes the red line normal to the prism.)
    • Rotate the small green circle clockwise until the green line is directly on top of the light beam. (In the image above, the angle of refraction is being measured.)
    1. What is the measure of the angle of refraction?
    2. What is the measure of the angle of incidence? (You will need to rotate both the green line and the red line in the angle tool to find this.)
  3. A critical angle is defined as the smallest angle of incidence for which light does not "escape" the prism. (The critical angle leads to an angle of refraction of 90°.) When the angle of incidence is larger than the critical angle, total internal reflection occurs.
    1. With n = 1.50 and λ = 500 nm, vary any other parameters in the Gizmo. What is your best estimate for the critical angle when n = 1.50?
    2. Estimate the critical angle when n = 1.20.
    3. Estimate the critical angle when n = 2.00.
  4. Extension: When light travels from one medium into another, the amount of refraction is described by Snell's Law: n1sinθ1 = n2sinθ2
    • n1 = the index of refraction of the first medium
    • n2 = the index of refraction of the second medium
    • θ1 = the angle of incidence
    • θ2 = the angle of refraction
    1. First, substitute the angle of incidence and the angle of refraction that you measured in questions 2a and 2b into Snell's Law. Evaluate and verify that the equation is true.
    2. If your values were off by a little bit in the previous question, why do you think that might be true?
    3. Substitute n1 = 1.20, n1 = 1.50, and n1 = 2.00 into Snell's Law. Calculate the critical angle in each case. (Use θ2 = 90° and solve for θ1.) How close were your earlier estimates?
    4. Use Snell's Law to calculate the critical angle when n1 = 1.75. Check your answer in the Gizmo.