Applets: Resolution, 2-Slits, N-slits

1. Resolution: These are movies of simulations. Play each and say how varying each parameter causes the resolution to change.

     http://webphysics.ph.msstate.edu/jc/library/24-7a/    hole size changes

     http://webphysics.ph.msstate.edu/jc/library/24-7b/    source separation changes

     http://webphysics.ph.msstate.edu/jc/library/24-7c/    wavelength changes

Resolution is expressed as the angular separation, theta, of 2 point objects that can just be resolved (based on the Rayleigh criterion). Write a proportionality that shows how the value of theta is related to the three parameters above:

        theta        is proportional to    _____________________
   
Thus,         theta = 1.22 * __________________                where 1.22 is the proportionality constant.

2. Let the aperture have N identical slits, each having the same small width, a, with the center-to-center spacing from one slit to the next slit being the same value, d, for all slits.
The applet http://www.physics.yorku.ca/undergrad_programme/highsch/Line.html (works on Mac) shows the case for N = 3 and N = 4 slits. Scroll down until the "Clear screen=0" line is at the top of the viewing area [Be certain that you can see the graph being plotted below the phasors]. Enter 0 in the first box, then click "Draw Phasor." Three phasors will appear, rotated by 10° from each other, along with the phasor sum (in blue). A dot will appear below the box showing the intensity for this phase difference. Each time you click "Draw Phasor" the phase angle will increse by 10°. To reset the simulation you must reload the page.

Try this and experiment until you think you understand phasors! Now draw phasors that will help explain why a single slit or 4 slits acts as they do.

[Bonus: fill in the table on the back of the page.]

3. This one allows you to change the number of slits and see the intensity pattern.
    http://www.physics.nwu.edu/ugrad/vpl/optics/diffraction.html   
• You can change the parameters by typing into the boxes. Can look at n-slit pattern for any value of n, but it only seems to work correctly for n<=10. Type, then hit "enter" to see change.
• Checking "pure single slit" causes the diffraction envelope [single slit pattern] to be displayed.
• Checking "pure n-slit" causes the ideal point source [slit-width = 0] pattern to be displayed.
• Checking only "complete pattern" shows the graph of intensity vs. position that you expect for a set of real slits.

What do you predict will happen as we make the slits very narrow and increase the number to, say, 1000? Sketch the approximate pattern below.

4. Bonus: related to #2. Case of 3, 4, ... N slits

Let the aperture have N identical slits, each having the same small width, a, with the center-to-center spacing from one slit to the next slit being the same value, d, for all slits.

The applet http://www.physics.yorku.ca/undergrad_programme/highsch/Line.html (works on Mac) shows the case for N = 3 and N = 4 slits. Scroll down until the "Clear screen=0" line is at the top of the viewing area. Enter 0 in the first box, then click "Draw Phasor." Three phasors will appear, rotated by 10¡ from each other, along with the phasor sum (in blue). A dot will appear below the box showing the intensity for this phase difference. Each time you click "Draw Phasor" the phase angle will increse by 10¡. To reset the simulation you must reload the page.

The phasors represent the amplitudes of the waves, with each slit contributing an amplitude of 1. Remember that the intensity is the square of the amplitude. Use the applet to help you fill in the table below for 3 slits. Scroll down the page to find the applet for 4 slits, and fill in the table for 4 slits. Try to predict the case for 5 slits.

This page maintained by Anne G. Young. Last modified 20-Apr-2005 .