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The intensity pattern from the two slits for a single wavelength looks like the

ID: 2154956 • Letter: T

Question

The intensity pattern from the two slits for a single wavelength looks like the one shown on the left side of the figure.

If another slit, separated from one of the original slits by a distance , is added, how will the intensity at the original peaks change?

By examining the phasors for light from the two slits, you can determine how the new slit affects the intensity. Phasors are vectors that correspond to the light from one slit. The length of a phasor is proportional to the magnitude of the electric field from that slit, and the angle between a phasor and the previous slit's phasor corresponds to the phase difference between the light from the two slits. Recall that at points of constructive interference, light from the original two slits has a phase difference of , which corresponds to a complete revolution of one phasor relative to the first.

Notice that, as shown in the figure, undergoing a complete revolution leaves the phasor pointing in the same direction as the phasor from the other slit. Think about the phase difference between the new slit and the closer of the two old slits and what this implies about the direction of the phasor for the new slit.

The peak intensity increases.

Part D
Are there any points between the maxima of the original two slits where light from all three slits interferes constructively? If so, what are they?
No
Yes, halfway between the original maxima
Yes, at intervals one-third of the distance between the original maxima
Yes, halfway between every second pair of maxima

IMAGE

http://session.masteringphysics.com/problemAsset/1001488/11/117799.jpg

Explanation / Answer

Part C:

The peak intensity increases.

Part D:

No

Explanation:

Since the original two slits do not interfere constructively anywhere except for the original maxima, it would be impossible for all three slits to interfere constructively somewhere between the original maxima. However, there are two places between the maxima where the intensity is zero, instead of just one such minimum as in the case of just two slits. This means that the intensity dies off more quickly as you move away from one of the peaks than it would for two slits, and then stays low until the next peak is reached.

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