Using Phasors to Graph Intensity vs Angle (4 slits)

[Casebur]

3.a) Use phasors to sketch the intensity vs. angle for a 4-slit interference pattern (identical
width and separation d=5 microns, wavelength =0.5 microns.)

b) On the same angular scale, draw the intensity pattern if the top two slits are covered.

c) The intensity pattern if the bottom 2 slits are covered is the same as (b), of course. So
you can consider the top and bottom pairs of slits as two sources that have an angularly
dependent radiation pattern. These two sources interfere with each other, and they are
separated by 2d (center to center.) Draw, on the same angular scale, the intensity pattern
for interference of two uniform slit sources separated by 2d. If you multiply this by your
pattern in (b), you should get your pattern in (a).

d) Now consider the interference pattern from just the top and bottom slits, which have a
separation of 3d. (Cover the two middle slits.) Sketch, on the same angular scale, this
pattern. Are the zeros of intensity at the same angles as in (a)? Discuss why or why not.

Hey, I have been working on this problem for a while now and am not sure where to start,

so far I have dsin(θ)=mλ and i calculated the angle to be θ=asin(.5μ/5μ) which gave me a value of 5.74 degrees. am i on the right track?

Any help on how to move forward will help a lot!
Thanks

 

[jbsteele]

!Yes, you are on the right track. The next step is to use phasors to sketch the intensity vs angle for a 4-slit interference pattern. You can do this by using the same equation you used to calculate the angle: dsin(θ)=mλ. The m value is the order of interference, which ranges from -2 to 2. For each value of m, you need to calculate the angle and then draw a phasor of the corresponding intensity at that angle. Once you have all 4 phasors drawn, you should be able to get the entire interference pattern.