# Two-Slit Wave Model

Science Snack
Two-Slit Wave Model
Use index cards to show how light plus light equals dark.
Two-Slit Wave Model
Use index cards to show how light plus light equals dark.

By experimenting with this model of light-wave addition, you can understand the behavior of light as it passes through two narrow slits. Why do two sources of light sometimes combine to make bright spots and sometimes dark? It’s all a matter of phases.

Tools and Materials
• Twenty-five 3 x 5 index cards (approximately 75 x 125 millimeters)—we’ll call these “smaller cards”
• Seventeen 5 x 7 index cards (approximately 125 x 175 millimeters)—we’ll call these “larger cards”
• Masking tape that is 1/2 in (1 cm) wide; the narrower the better
• Transparent tape
• Blue and red marker pens
• Scissors
• Pencil (not shown)
• Optional: String (not shown)
Assembly

Note: Prior to doing this activity, we recommend you try Two-Slit Experiment to observe an interference pattern. Together, these two Snacks will help you move from observing the two-slit interference phenomenon to understanding the science behind it.

For this activity, you'll need to first make a sine-wave template, and then use the template to create a set of cards with sine waves drawn across both sides.

Use this trick to draw more accurate sine waves:

1. Take one of the small index cards and fold it in half lengthwise (hot dog fold). Unfold the card. Now fold the card in half along its width (hamburger fold). Leaving that fold in place, fold the card in half again. Unfold the card. You should see a long fold mark lengthwise across the middle, and three shorter fold marks across the width of the card. The card should be divided into eighths.
2. Mark a point on the crosswise fold mark nearest the left edge, about 1/2 in (1.25 cm) down from the top of the card—your maximum.
3. Along the bottom of the card, mark a point on the right crosswise fold mark, about 1/2 in (1.25 cm) up from the bottom—your minimum.
4. Draw the sine wave starting at the center-left side of the card moving through the maximum, then back through center, and through the minimum point ending at the center-right side of the card.
5. Using scissors, cleanly cut along the sine wave that you’ve drawn. The top half and the bottom half produce two sine-wave templates—give one to a friend.
6. To use this template, line up the bottom of the template with the bottom of a new card and, using a blue marker, draw along the wave edge. Repeat until you have created twenty-four cards with matching blue sine-waves drawn on them.
7. You'll need sine waves on the back of the cards too, so flip both your blue sine-wave template and the smaller cards over on a horizontal axis (from top to bottom) and draw a sine wave on the back that starts at the center of the left edge of the card and move downwards. (If you hold the card up to a light, the wave on the front and the wave on the back will coincide.)
8. Using transparent tape, tape the smaller cards together into two straight rows of twelve cards each, making sure that all the sine waves move upwards from the left side (following the original pattern of the template before you flipped the cards over). It’s important that the sides of the cards touch but don’t overlap.
9. Once you've finished making your two sets of blue sine-wave cards, follow all of the steps above again with the larger cards to make two sets of red sine-wave cards with eight cards each.

Make a model of two slits:

1. Tear off several long strips of masking tape. Tape them in a line on the floor, leaving two small slits that are approximately two "blue" wavelengths (10 inches or 25 centimeters) apart.
2. Tear off another long strip of masking tape, about two meters in length. Tape this down so it is parallel to and about five “blue” wavelengths (25 in or 55 cm) away from the other tape. This strip represents your screen.
To Do and Notice

Compare the blue and red sine-wave cards. Notice the difference in length between the blue and red waves. The red light waves will be longer than the blue. You have made a good model of red and blue light waves.

Look at any sine-wave card and notice three important points: the maximum (highest point), the zero crossings (where the wave crosses the middle line of the card, including at the leading and trailing edges), and the minimum (lowest point). Scientists describe these points using the term phase. When two waves add up “out of phase,” this means the highest point of one wave lines up with the lowest point of the other, canceling out the light. When waves add up “in phase,” this means the highest point of one wave lines up with the highest point of the other, strengthening the light.

Consider a light source like a laser shining into the two slits. The waves come into the slits in phase, oscillating together.

Take one strip of blue sine-wave cards and line it up with the center of one slit. Take the other strip of blue sine-wave cards and line it up with the center of the other slit. Make sure the two strips begin in phase at the slits. Unfurl both card strips towards the “screen” (second tape line), angling them so they cross the screen together at a point opposite the midway point between the two slits. Notice that both waves have the same phase at the screen. They add together in phase, producing a bright spot where they meet on the screen. Make a blue mark at this point on the tape (see photo below).

Investigate other points on the screen, by stretching the strips from each slit to intersect at different places along the screen. Try to find a point where the two strips arrive out of phase. Here the light will be canceled, creating a dark spot. Make a black mark at the intersection point on the tape and draw a blue circle around it to note this is where blue light cancels out (click to enlarge the photos below).

Repeat the experiment using the red sine-wave cards. Notice and mark the locations of the bright regions and the dark regions (see below).

After you’re done investigating both the blue and red sine-wave cards, change the distance between the slits, and repeat the experiment with fresh pieces of tape.

What's Going On?

Both waves start out together with the same phase and travel the same distance to the center of the screen (the halfway point between the two slits), so they have the same phase when they add together. There is thus a bright spot in the middle of the screen. When one wave travels one‐half of a wavelength further than the other, the lights cancel and create a dark region.

There are additional bright and dark regions that stretch out in both directions from the center. When the two light paths differ by an integer number of wavelengths, the waves arrive in phase and make a bright spot. When they travel an odd integer multiple of a half-wavelength, they add up out of phase and create a dark spot.

Going Further

Since red and blue lights have different wavelengths, the distance between adjacent red maxima is different than the distance between adjacent blue maxima. The spacing between adjacent maxima is usually measured as an angle with its vertex halfway between the two slits. If the wavelength of the light is L, and the distance between the slits is d, then maxima occur when the angle, T, is an integer multiple of L/d