B Explanation for bright fringes in Single Slit Diffraction

AI Thread Summary
The discussion centers on the confusion surrounding the formation of bright fringes in single-slit diffraction compared to the more straightforward double-slit experiment. Participants express difficulty in understanding why certain points interfere constructively while others do not, particularly at odd multiples of half-wavelengths. The central position is identified as the most favorable for constructive interference, leading to maximum intensity, but the reasons for this remain unclear. The conversation also touches on the conditions necessary for applying Fraunhofer diffraction and the implications of Fresnel diffraction. Overall, the complexity of the underlying mathematics and the lack of intuitive explanations for bright fringes in single-slit diffraction are highlighted.
Aurelius120
Messages
269
Reaction score
24
TL;DR Summary
The formula for position of bright fringes of Single Slit Fraunhoffer diffraction is given by $$a\sin(\theta_n)=\frac{(2n+1)\lambda}{2}$$
$$\theta_n \approx \sin(\theta_n) \approx \tan(\theta_n)=\frac{x_n}{D}$$
##n=1,2,3,......##
Looking for an intuitive explanation for this formula.
The central bright fringe is brightest. Why?
In Young's Double Slit Experiment, we were shown the complete derivation for location of fringes, width of fringes etc. on interference by two point sources of light and all was well.
In Single Slit Diffraction we were just asked to remember the formulae as they were with little explanation.

I understand that all waves from points equidistant from slit-center on either side interfere constructively at the screen-center but why don't they cancel with waves from points that are in opposite phase? Why are waves from every point interfering constructively with waves from every other point? If there is a combination of both constructive and destructive, why is it brighter than other bright fringes?

A little research gives a clear explanation for dark fringes and why they are formed at path difference of ##n\lambda##. For example here.

However I cannot find an explanation for formation of maxima at ##\Delta x=\frac{(2n+1)\lambda}{2}##? Is the explanation intuitive or is the reason purely mathematical?(perhaps too complicated to be taught)
 
Physics news on Phys.org
BvU said:
Although there is a progressive change in phase as you choose element pairs closer to the centerline, this center position is nevertheless the most favorable location for constructive interference of light from the entire slit and has the highest light intensity if the Fraunhofer diffraction expression is reasonably applicable. If the conditions D >> a and D>> a2/λ are not met for this combination of slit width and screen distance, the Fresnel diffraction result may not have maximum intensity on the centerline.

Still don't understand why it is brightest?
1000016216.jpg

A and B will interfere constructively with each other but destroy C and then other points on either side will destroy whats left. It will be a Central Dark Fringe , Right?

And still don't see why bright fringe at odd multiples of half wavelength
 
I'm looking at the bottom half of lecture notes (Prof. Dmitri Pogosian, Alberta Ca), based on Young and Freedman, 12th ed. (I only have 11th ed, pp 1369...1376) and really don't know what to add.

And there's always the hyperphysics explanation (4 pages, phasors, etc)

Aurelius120 said:
In Young's Double Slit Experiment, we were shown the complete derivation for location of fringes, width of fringes etc. on interference by two point sources of light and all was well.
Note that there too the single-slit pattern appears -- as an envelope

##\ ##
 
Thread 'Question about pressure of a liquid'
I am looking at pressure in liquids and I am testing my idea. The vertical tube is 100m, the contraption is filled with water. The vertical tube is very thin(maybe 1mm^2 cross section). The area of the base is ~100m^2. Will he top half be launched in the air if suddenly it cracked?- assuming its light enough. I want to test my idea that if I had a thin long ruber tube that I lifted up, then the pressure at "red lines" will be high and that the $force = pressure * area$ would be massive...
I feel it should be solvable we just need to find a perfect pattern, and there will be a general pattern since the forces acting are based on a single function, so..... you can't actually say it is unsolvable right? Cause imaging 3 bodies actually existed somwhere in this universe then nature isn't gonna wait till we predict it! And yea I have checked in many places that tiny changes cause large changes so it becomes chaos........ but still I just can't accept that it is impossible to solve...
Hello! I am generating electrons from a 3D gaussian source. The electrons all have the same energy, but the direction is isotropic. The electron source is in between 2 plates that act as a capacitor, and one of them acts as a time of flight (tof) detector. I know the voltage on the plates very well, and I want to extract the center of the gaussian distribution (in one direction only), by measuring the tof of many electrons. So the uncertainty on the position is given by the tof uncertainty...
Back
Top