# University of Wisconsin Green Bay

A laser shines through a double slit apparatus forming a pattern of dots on a screen 1.5 m away. The two slits are 0.10 mm apart and the dots on the screen are 8.3 mm . What color is the laser light?

• You might immediately recognize this as an interference problem because of the reference to a double slit apparatus. However, it is worth recognizing the deeper underlying physics. If you think about the reason for the bright and dark spots, you will realize that the dots form a standing wave pattern due to the interference of rays of light from each opening.

As you can see in the picture below, light diffracts when it passes through each slit and so rays of light radiate out as if each slit was a source of light. The two rays that reach any single point on the screen (such as is indicated by the red dot on the drawing) interfere constructively to give a dot of light or destructively to leave a dark, or unlit, region on the screen.

• To picture the experimental set up in the problem, first locate the double slit apparatus and the screen. It may also help to draw dots of light and dark on the screen so you can visualize the interference pattern. Then draw the two interfering rays that reach the point you need to consider. Finallly, the dotted lines on the drawing will help you understand the geometry that is used to define angles and locations.

• Whenever a standing wave pattern comes about because of double slit interference, bright spots and unlit spots can be located according to the equations

• At this point, you will recognize that you have one equation but two unknowns. You want to solve for wavelength so that you can learn color, so there must be other information in the problem that can help you find θ. You can see the triangle you need in the simplified drawing below.

From this drawing, you can see that tanθ = (8.3 x 10-3m)/(1.5 m) = 0.0055. θ = 0.3170.

You can look up this wavelength of light in your text book or on line to find that the laser must be green.

• The bright and dark spots you see on the wall after the laser goes through a double slit grating result from the interference of the two beams created by the openings. This is therefore a standing wave pattern. The double slit interference equation includes all of the geometry showing where waves are in or out of phase. As long as you understand the symbols in the equation and how each side related to path length, you can work the problem in a straightforward fashion. In this case, the distances provided allowed you to find θ, and once you found wavelength you could determine color.

The statement of the problem implied that the answer should be in the visible range of light, and, indeed, you found that a laser that produces this pattern must be green light. If you have seen this set up in lab or lecture, you also know that the fringes (colored bands) are very close together as the problem suggests.