Single Slit Diffraction Patterns: When & Why?

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    Diffraction Patterns
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Discussion Overview

The discussion focuses on the conditions under which single slit diffraction patterns occur, specifically the applicability of the formula sin(theta)=(lambda)/b. Participants explore whether this phenomenon requires light to be focused through a lens or if it can occur with light simply projected onto a screen.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants question the necessity of focusing light to observe single slit diffraction patterns, citing differing interpretations from textbooks and presentations.
  • One participant notes that diffraction occurs when the wavelength of the incident wave is larger than the slit width.
  • Another participant states that modern texts do not discuss the focusing of light in relation to diffraction.
  • One contributor explains that Fraunhofer diffraction theory assumes a planar incident wave, which can be achieved either by focusing light or by collimating the beam.
  • Participants discuss the reason for the formation of patterns, attributing it to path length differences and interference among wave parts passing through the slit.
  • There is a question about why intensity reaches zero and then increases again, which is attributed to the transition between constructive and destructive interference.
  • One participant inquires about the nature of wave propagation, asking if waves can travel in curved paths.
  • Another participant mentions that photons follow straight lines, but can change direction during absorption and emission processes.
  • There is a request for an explanation regarding why waves can "turn the corner" when diffracted, leading to a reference to Maxwell's equations and Huygen's principle as explanations for wavefront behavior.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of focusing light for diffraction patterns, and the discussion contains multiple competing explanations for the observed phenomena. No consensus is reached on these points.

Contextual Notes

Some assumptions about the definitions of terms like "planar wave" and "collimated beam" are not fully explored, and the discussion does not resolve the mathematical implications of the diffraction formula.

PhiJ
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When do single slit diffraction patterns occur (i.e. when is the formula sin(theta)=(lamda)/b applicable)? Is it only when the light gets put through a lens and focused on a single point at different angles, or is it generally. My textbook derives it for when the light is focussed, but my teachers presentation says that it is for if you just show the light on the screen without focussing it.
If this is true, could somebody derive it for me please?

Thanks, PhiJ
 
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PhiJ said:
When do single slit diffraction patterns occur (i.e. when is the formula sin(theta)=(lamda)/b applicable)? Is it only when the light gets put through a lens and focused on a single point at different angles, or is it generally. My textbook derives it for when the light is focussed, but my teachers presentation says that it is for if you just show the light on the screen without focussing it.
If this is true, could somebody derive it for me please?
Thanks, PhiJ

diffraction occurs when the magnitude of the wavelength of the incident wave, is bigger then the magnitude of the opening (ie the slit).

marlon
 
There's no discussion over "focussing" in modern texts treating diffraction whatsoever.

Daniel.
 
But WHY do you get PATTERNS from a single slit?

btw, how do you do greek on this forum, do you just have to copy it from word?
 
Fraunhofer diffraction theory assumes a planar incident wave. One way of obtaining a planar incident wave is by focusing the light and placing the aperture at the focus. The theory of Gaussian beams tells us that the curvature of the field is exactly zero at the focus. The advantage of using this method is that a brighter diffraction pattern will be obtained.

A second way of acheiving a planar wavefront is by simply collimating the beam (i.e. focusing at a distant object). The advantage of using this method is that the placement of the aperture is not critical since the curvature of the wavefront is close to zero along the length of the collimated beam.

So essentially the textbook and your teacher are describing two different methods of achieving a planar wavefront. In summary, how you obtain the planar wavefront is not critical. Both methods can be used with success to obtain a Fraunhofer diffraction pattern.

Claude.
 
PhiJ said:
But WHY do you get PATTERNS from a single slit?
btw, how do you do greek on this forum, do you just have to copy it from word?

in an very easy/intuitive language, you get patterns because when the wave passes through the slit, it gets a pathlength difference between the parts of the wave at the top and bottom of the slit (ie different distances to be crossed if you want them to come together at the same point). This leads to interference between the different "parts" of the wave.

You see ?

marlon
 
But the patterns you get at the other end of the slit, why does the intensity of light reach a zero and then increase again afterwards?
 
PhiJ said:
But the patterns you get at the other end of the slit, why does the intensity of light reach a zero and then increase again afterwards?
that is the transition from constructive to destructive interference and back.

see this

marlon
 
  • #10
Nearly get it. Can waves travel in bendy lines, or only straight?
 
  • #11
PhiJ said:
Nearly get it. Can waves travel in bendy lines, or only straight?


err, what exactly do you mean ?

If you are talking about changing direction, the wave does not do this "automatically".

In particle language, photons can 'change" in absorption/emission phenomena , if the incident dirction of the absorbed photon is different from the direction of the emitted photon. Keep in mind that these are not the same hoton, though. A photon itself does always follow a straight line because it's resmass is 0.

marlon
 
  • #12
Thanks, I get it now.
:smile:
 
  • #13
Wait... Why can the wave turn the corner when diffracted. Do we just have to say 'it does' or is there an explanation?
 
  • #14
There is an explanation - Maxwell's equations. Every electromagnetic phenomenon is derived from them, including optical phenomenon.

A good description of what happens to wavefronts as it passes through the aperture is described by Huygen's principle.

Claude.
 

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