Questions of single slit diffraction

[toesockshoe]

Homework Statement

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.

Homework Equations

look below

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 don't think that's right. Suppose you only had 2 phasors... the angle between the 2 phasors ISNT B/2 (or 5pi/6) ...its 5pi/3 because there's 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?

 

[TSny]

Suppose you only had 2 phasors... the angle between the 2 phasors ISNT B/2 (or 5pi/6) ...its 5pi/3 because there's only 2 phasors, the angle between them is the same as the angle between the first and last vector.

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.

 

[toesockshoe]

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.

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

 

[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.