## What Can We Learn About Velocity From Light? Doppler Effect

**Overview:** Instructor connects the particle and wave model of light, and students explore the Doppler effect using an online applet.

**Physical resources:** Balloons, shallow pan of water

**Electronic resources:** Doppler effect applet

**Instructor contrasts the particle and wave model of light:**

- Instructor defines "field": A mathematical model which predicts the force felt by charged particle (which predicts how it will move) at any point in space, based on where other charged particles are located. (Video introduces the slightly too generic "A description of how charged particles interact with other matter.")
- Observation and demonstration of electromagnetic field: Put a charged balloon near the hairs on your arm to "feel how the field changes" as you move the static charge on the balloon.
- Observation: Shallow water pan as a 2D analogy for waves, to observe the waves travel outward from a "source". Point out the crests and troughs. Draw wave from the side to explain wavelength.
- The different models of light are useful in different situations. For example, "flux and luminosity" only make sense as counts per cm
^{2}per second and counts per second using the particle model, and the Doppler effect makes sense only using the wave model, but the idea of reflection and "light travels outward in all directions with constant speed" makes sense using either model. - Introduce Quantum mechanics (a model of the behavior of really small things) and resulting Planck relation E_photon = h*c / lambda as a "bridge" between the particle model and wave model of light.
- Notes: (wave model, fields QM)

**Application of wave model of light: Doppler effect applet**

- Students open applet: Applet: Doppler Effect
- After quick demonstration of applet, give student challenge:
- Compare the wavelength observed by an observer standing at the right hand edge of the applet screen when waves reach them from four different sources which are (A) not moving, (B) moving toward observer, (C) moving away from observer, (D) moving perpendicular to observer. Compare these to the wavelength emitted from the source (measured by freezing simulation when the source is not moving).
- Have students stop applet (ctrl-s) and actually make measurements by transferring the wavelength measurement to the edge of a piece of paper held up to the screen.
- Make a chart of lambda_observed compared to lambda_emitted for each case (greater than, less than or equal to?)
- Summary of student results: (doppler observations)

- Instructor explains that this is a simulation of the light emitted from a moving object. Introduce hypothetical situation of light made of photons of only one energy being emitted from sources moving in the same directions as in the observations they just made. Have students predict the energy of the observed photon in each of the same cases. Add a column comparing the energy of photon emitted to the energy of the photon observed in each case. (i.e. They must make prediction using the Planck's formula connection between the two models.)
- Summary of student results: (doppler observations)

- Ask students to observe the observed wavelength for an object moving away from the observer at a slow, intermediate and fast speed. Have them put these three situations in order from longest to shortest observed wavelength.
- Diagram showing relation of wave crests to observed change in wavelength: (fields QM)

- Introduce mathematical description of this relationship: lambda_observed - lambda_emitted / lambda_emitted = v / c = z = redshift

**Teacher tips/tricks:**

- With Doppler applet, be sure to warn students not to have their source movement create a red arrow. This represents "faster than the speed of light motion" and will not show the patterns we seek.
- Make sure the idea of the shift in observed wavelength for motion toward and away is clear, before introducing the more subtle idea of the change in
**amount**of shift, based on the speed of the motion.

**Assessment ideas:**

- Use the particle model of light to explain the Doppler Effect. (This is really hard to do and doesn't make sense: the photons "magically" lose energy. This can lead to a deeper discussion of the usefulness of models in different situations.)
- Arrange each of these situations from shortest observed wavelength to longest. (Source and observer moving in different directions with same speed.) Image of example situations: (doppler situations)
- Why do astronomers call the quantity z = v / c "redshift?"