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# 4.2: Activities

## Things You Will Need

All you will need for this lab is this PhET simulator. Go ahead and run this simulator now in another window for use in the activities below.

## Using the Simulator

This software simulates wave interference of various types. We will be focusing on interference of light passing through a double slit. We therefore configure the simulator as follows:

• select the window "Slits"
• click the light source button
• select the "Screen" check box, and the "Intensity" sub check box
• select "No Barrier" in the drop-down menu
• set the "Frequency" slider somewhere near the middle of the red portion of the spectrum
• leave the "Amplitude" slider at its "max" setting

The green button on the Light Generator starts a plane wave, represented by alternating bright and dark regions that represent the crests and troughs of the waves, respectively. [Note that these do not represent bright and dark regions! That is, if you were in the simulator, and you looked at the Light Generator, you would see constant, uniformly-bright red light coming from it. If you run the simulator, this is in fact what you see on the screen.]

As with the simulators we have seen already, the pause button  halts the simulator, allowing you to more easily take measurements. In this lab, we will be taking only two types of measurements:

• distances with the tape measure , which can be dragged to anywhere it is needed – the base of the roll of tape will remain in place as you drag the other end (the length units for this tape measure is nanometers, which is $$10^{-9}m$$).
• times with the timer , which can also be dragged around (the time units in this timer is femtoseconds, which is $$10^{-15}s$$).

As we saw with a previous simulator, a powerful tool for precise time measurements is to pause the simulation, start the timer (it will not run until the simulation is restarted), and then continue the simulation one step at a time with the step simulator button.

## Computing the Light Frequency

You will notice that the slider for frequency of the light does not include a numerical output. Our task will therefore be to compute the frequency of the red light that you have chosen.  We will do this in several ways...

[Note: Our level of precision is such that if you use it in your calculations, you will want to use $$2.998\times 10^8\frac{m}{s}$$ for the speed of light.]

1. Measure the frequency of the light in two ways. In each case, explain what you measure and how you determine the frequency from it.
1. using only the timer (note the "step simulator" trick given above)
2. using only the tape measure (clicking the "Graph" check box for the purposes of this measurement may be helpful).
2. These two calculations are not likely to agree exactly, so let's estimate some uncertainty.
1. The timer measures in hundredths of femtoseconds, but when the simulator is stepped, it doesn't increment the timer by one unit in this decimal place, so the real time elapsed falls somewhere in a range. Compute the percentage uncertainty of your time measurement using the appropriate range.
2. The tape measure measures down to tenths of nanometers, but dragging the tape measure the tiniest amount will jump the reading by more than this degree of precision, which means the actual length measurement falls somewhere in a range. Compute the percentage uncertainty of your length measurement using the appropriate range.
3. Determine whether your two calculations of the frequency of the light land within the uncertainty bounds.
4. Suppose that we want the most accurate measurement possible, using either of the two methods above. This means reducing the percentage uncertainty as much as possible. Explain how you would do this, and (assuming you didn't do this already), do so now for both methods, and determine the associated percentage uncertainties.

Next we will measure the frequency of the red light yet again (so don't change the frequency slider setting!), this time using what we know about double slit interference. This requires a few adjustments to the simulator:

• select "Two Slits" in the drop-down menu
• set the slit width to 500nm
• set the slit separation at 2000nm
• drag the double slit barrier as far left as possible, so that you mostly light after it passes through the double slit

Before freezing the simulator to take data, make sure it runs long enough to form an interference pattern on the screen.

[Helpful hint for making two length measurements with a common point involved: Place the base of the tape measure at the common point – it will stay put as you drag the open end of the tape measure to each of the other points in turn.]

1. Use the interference pattern to determine the light frequency by directly measuring the path length difference of the two interfering waves from the slits...
1. ... to a point of total destructive interference
2. ... to a point of maximal constructive interference
2. Determine the light frequency one more time, this time using Equation 3.2.3 derived in the LibreText for 9B (you can use either a dark or bright fringe). This requires a bit of work on your part, as there is no protractor provided by the simulator to measure angles.

## Fringe Spacing

You are probably finding that the calculations of the frequency are getting progressively worse. For question 3, this is because it is harder to make the measurement as accurately as in question 1. This is also true for question 4, but in that case the equation also drags in an approximation (see the text reference given in the Background Material for more details). We will conclude by looking at another approximation discussed in that text reference. If the angle of deflection is "small," then the separation of fringes (from dark to dark or from bright to bright) is given by a simple formula involving the wavelength $$\lambda$$, the distance to the screen from the slits $$L$$, and the slit separation $$d$$:

$\Delta y = \dfrac{\lambda L}{d} \nonumber$

1. Check this formula for the following conditions given (note that you have the wavelength of the light, as you are using the same light as in question 1), and comment on what these measurements say about the validity of this fringe-spacing formula. [Note: It is easier to measure the distances between the fringes in the simulator accurately using the intensity graph than the screen display.]
1. the settings you have currently (double slit barrier as close to the Light Generator as possible)
2. with the double slit barrier dragged closer to the screen (say at about the halfway point)

## Lab Report

Download, print, and complete this document, then upload your lab report to Canvas. [If you don't have a printer, then two other options are to edit the pdf directly on a computer, or create a facsimile of the lab report format by hand.]