Notes on running Mike Moloney's light simulations.               First Draft  February 27, 2001

All these simulations can be run by double-clicking them, but they all run full screen. Don't try to use Alt-Enter as I did to run in a smaller window, or you may lock up your laptop like I did.

Refraction simulation

This simulation initially shows two sources of light. These sources are at each end of the white arrow, so you can think of them as the ends of a slender object in the lower medium. (If you want the lower medium to be water, change its index to 1.33.) Notice that the black arrow represents the approximate point from which the rays appear to be coming after they are refracted at the surface. That is, the black arrow represents approximately the position and orientation of the image of the white arrow.

The white arrow is the true position of the object and the black arrow is the apparent position of the object. You can move each end of the white arrow around by dragging with the mouse, so that you change the position of the object. (The ends will merge if you get them too close. In this case you can go to one source (bottom slider) then drag the source away from where it was, then go back to 2 sources, and this should give you the white arrow back again. Otherwise, you could just restart the simulation by pressing <Esc> and then <y>.

From each source a bundle of rays emerges and reaches the surface. At the surface each ray is refracted and reflected, but the simulation shows only the refracted ray unless the critical angle is exceeded, then only the reflected ray is shown (beyond the critical angle).

Suggestions for running the simulation.

• Try changing the main angle.
• You will see the rays refract more, and then at about 40 degrees some rays begin to be totally internally reflected. You will also see the image changing drastically. When the angle is nearly zero, the image (the black arrow) is vertical and closer to the surface than the object (the white arrow). But! When you increase the angle, you will find a couple of things happening to the image! See if you can relate what happens here to your view as you look down into a quiet swimming pool, or a flat pan of water. Can you name two distinct changes in the character of the image as the angle is increased?
• Try dragging each end of the object (the white arrow) so it is closer to the surface and parallel to the surface. Then increase the main angle until you get some total internal reflection. Make an estimate of the critical angle, and then check it from snell's law n1 sin (theta 1) = n2 sin (theta 2). [Hint: what angle do we have to the normal in the upper medium when total internal reflection occurs?]

Lens and Mirror Simulation.

This lets you play with i) a single object and two lenses, or ii) a single object and one spherical mirror.

Common features of the simulation are: real images are red, and virtual images are light green. Real light rays are white, and extensions of these rays are green. (The green rays indicate where the white rays appear to come from, or appear to be going to.)

Red divisions denote 10 units (pixels) and yellow units 50. For the lenses, small blue blocks show the location of the focal point.

The mouse position is given in yellow in the lower middle of the screen.

In each simulation, you can drag the head of the object (where the tip of the arrow is) to move the object around. You can drag the mirror with the mouse, but to move the lenses, or change their focal lengths, you must use the sliders.

In the mirror simulation, you can drag the object around by its 'head' and if you run too close to the mirror, the object gets 'stuck' to the mirror. Then the question is how to get the object 'unstuck' from the mirror. Try to figure that out. [See answers below if not.]

Suggestions for Running the Lens Simulation

• Bring up the lens simulation initially.
• Say if the image formed in the first lens (the first image) is real or virtual.
• Grab the head of the object and move it slowly closer to the lens.
• Notice what happens to the image position as the object gets closer to the lens.
• What happens when the object is right at the lens's focal point?
• What happens when the object gets closer than the lens's focal point? Is the image the same kind as it was before?
• The magnification formula is -i/o, where i is the image distance and o is the object distance.
• Drag the object to x=120, then release the mouse button. Notice that as you move the mouse around not holding the button down, you can read off the mouse's position in yellow in the lower middle of the screen.
• Record the x and y positions of the object (the tip of the arrow). Do the same for the image formed by the first lens. Calculate i and o by using the fact that the lens is located at x=200 (or this is when the simulation first comes up. This means you can calculate -i/o, but how do you check that m= -i/o? You have to be able to figure out from your readings what m is. When you have done this, you should agree with the formula except for the minus sign. What does that sign mean?
• Can you make the image of the first lens be a 'virtual object' for the second lens? [Hint: To do this, the image of the first lens must occur to the right of the second lens.]

Suggestions for Runnng the Mirror Simulation

• Do you know why the rays from the object 'bounce off' the mirror without touching it? (They bounce along a vertical line up from the vertex of the mirror.) See Crummett and Western p. 989, Fig 36.11 for the answer.)
• Try getting 6rays and spread them out over a 30 degree angle. Movc the mirror all the way to the right. Now move the object to the left and maneuver the object until one of the rays from the object appears to bounce straight back from the mirror. The place where this ray crosses the axis (the horizontal black line) is the center of curvature of the mirror. The focal length of a mirror is supposed to be half the radius of curvature. Check this by seeing if the distance from the center of curvature of the mirror to the mirror vertex (this is the radius of the mirror) equals twice the focal length.
• Four rays
• In the paraxial approximation, there should be four easily-drawn rays which converge to form the image.
• The ray through the center of curvature, which bounces back.
• The ray which strikes the vertex (where the mirror meets the axis) and bounces back at the same angle
• The ray going in parallel to the axis and coming out through the focal point.
• The ray going in through the focal point and out parallel to the axis.
• Go to 12 rays spread over 30 degrees and see how close you can get to finding all four of these rays by moving the head of the source around. You may want to play with the main angle as well, or shift the angle spread around.
• Since 1/i + 1/o = 1/f, if we put the object at the focal point, i becomes infinity. That is, if the object is at the focal point, rays from object should all be travelling parallel after striking the mirror. (The supposedly will meet at infinity.)
• Move the object until the rays leaving the mirror are nearly parallel. Chcek that the object's distance from the mirror vertex equals the focal length of the mirror.
• If we have a mirror concave toward the object, its focal length and radius are positive.
• Over what range of object distances from the mirror do we get real images? Check this out by moving the object.
• Over what range of object distances from the mirror do we get virtual images? Check this out by moving the object.
• If we have a mirror convex toward the object, its focal length and radius are negative.
• Over what range of object distances from the mirror do we get real images? Check this out by moving the object.
• Over what range of object distances from the mirror do we get virtual images? Check this out by moving the object.

Grating Simulation.

This lets you 'see' the waves coming out of a grating, and move the angle around to see at what angles the waves 'get in step'. You can adjust the number of slits in the grating between 2 and 6. When you move the angle and it looks like the waves are in step, call for an intensity plot, and see if it gets bright at the angle you selected.

Suggestions:

• From the initial screen when the simulation first comes up, try changing the wavelength until the 'extra path' until the waves are in step equals one wavelength.
• What wavelength is this?
• From the 30 degree angle and the extra path of one wavelength, you should be able to tell how many wavelengths apart the two slits are. [See below for the answer]
• Now try clicking 'Do Intensity Plot'. You should see a bright area around 30 degrees.
• Change to 4 slits and then do another intensity plot. This time the bright area at 30 degrees is a lot narrower than when you used two slits.
• What do you think will happen when you go to 6 slits? Still narrower, or wider?
• Can you say in words why the bright area around 30 degrees changes?
• In between the bright areas for 4 slits there are two somewhat-bright areas. If you went to 3 slits, how many somewhat-bright areas would there be?
• Try changing the delay slider from 0 to 20 degrees or so. This changes the phase of the waves coming out of the 'delay' region. You should be able to see that the bright areas change around, occurring at different angles.
• Can you explain why putting a delay between each wave shifts the angle of a bright area?
• Try adjusting the wavelength and try to find the wavelength which will shift the beam around the most when you put in a phase delay of +90 degreees.
• Can you explain why this wavelength means a larger shift in angle?
• To get the narrowest bright area at 45 degrees, how many slits and what wavelength would you use?

Some Answers