# Questions of single slit diffraction

1. Mar 1, 2016

### toesockshoe

1. The problem statement, all variables and given/known data
I have a question on a practice midterm my professor sent out. I would ideally ask him, but I won't see him until itake my midterm. Instead I am attaching the question and solutions at attachments. THe question of interest is in the attachment "physics question" and the solution from the professor on "physics answer"

The question I have a problem with is number 1b. (part b of the first problem). The part that asks you to draw a phasor diagram and and asks you what the intensity is.
2. Relevant equations

look below
3. The attempt at a solution

They said the total phase difference beta (the angle between the first and last phasor) is 5pi/3. so $$\beta = \frac{5\pi}{3}$$

Next they say that because there are 5 phasors, the angle between each phasor is pi/3 (because B/5 is pi/3). I dont think thats right. Suppose you only had 2 phasors.... the angle between the 2 phasors ISNT B/2 (or 5pi/6) ...its 5pi/3 because theres only 2 phasors, the angle between them is the same as the angle between the first and last vector. I think the correct formula for the angle between phasor is Beta/(n-1) where n is the number of phasors. Thus I think the angle between each phasor is 5pi/12, which makes drawing them slightly more complicated and finding the intensity though the diagram much more complicated.

If I am wrong, can someone correct me and tell me why?

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2. Mar 1, 2016

### TSny

When approximating the contribution of one region of the slit by one phasor, it seems reasonable to assign a phase angle for that phasor to correspond to the phase angle for a ray at the center of the region. If so, then when you are considering the angle between one phasor and the next phasor, you are considering the phase shift between the center of one region and the center of the next region.

3. Mar 1, 2016

### toesockshoe

im not sure what you mean center of the region. can you elaborate?

4. Mar 1, 2016

### TSny

The picture below shows a single slit divided into 5 sections. The light that goes through one region and heads toward the screen at a certain angle is represented by one blue ray which is drawn at the center of the region (red dot). Each blue ray can be represented by a single phasor. The phase difference between two consecutive blue rays determines the angle between two consecutive phasors.

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