Questions of single slit diffraction

In summary: The phase difference between two consecutive blue rays determines the angle between two consecutive phasors. If you want to approximate 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.In summary, the student has a problem with the first problem in the homework and thinks that the angle between each phasor is pi/3 instead of beta/(n-
  • #1
toesockshoe
265
2

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 [tex] \beta = \frac{5\pi}{3} [/tex]

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?
 

Attachments

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  • #2
toesockshoe said:
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.
 
  • #3
TSny said:
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?
 
  • #4
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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Related to Questions of single slit diffraction

What is single slit diffraction?

Single slit diffraction is a phenomenon that occurs when a wave, such as light or sound, passes through a narrow opening or slit and spreads out, creating a diffraction pattern. This pattern is a result of the waves bending and interfering with each other as they pass through the slit.

How does the width of the slit affect the diffraction pattern?

The width of the slit directly affects the diffraction pattern. A wider slit will result in a narrower central maximum and broader secondary maxima, while a narrower slit will result in a wider central maximum and narrower secondary maxima.

What is the difference between single slit and double slit diffraction?

The main difference between single slit and double slit diffraction is the number of slits present. Single slit diffraction occurs when a wave passes through a single narrow opening, while double slit diffraction occurs when a wave passes through two narrow openings at a fixed distance from each other.

How can single slit diffraction be used in practical applications?

Single slit diffraction is used in various practical applications, such as in spectroscopy to determine the wavelengths of light emitted by a source. It is also used in the production of holograms and in the design of certain optical instruments.

What factors affect the diffraction pattern in single slit diffraction?

The diffraction pattern in single slit diffraction is affected by several factors, including the wavelength of the wave, the distance between the slit and the screen, and the width of the slit. Additionally, the angle at which the wave hits the slit also plays a role in the resulting pattern.

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