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I was going through the standard derivation of intensity distribution in case of single slit diffraction Standard derivation of Intensity variation in single slit

I don't understand why we equate the scalar summation of electric field phasors(or the length of the phasor arc) to the Electric field at central maxima i.e. $E_{m}$, wouldn't that imply that the wavelets reaching any point are equal in number?

This doesn't make sense to me as using the Fresnel-Huygens principle for any point on slit we can see that the wavelets reaching a point on the screen at a higher angle would be comparatively lower than at a lower angle,in simplified terms due the the same arc length being distributed to a larger length of screen for higher angles.

Blz
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  • You can search Fresnel-Huygens principle on this site .... many issues with it ... but not bad for the 1800s or is it 1700s! A little embarrassing that it is still taught today ...Feynman's path integral is complex for high school. – PhysicsDave Nov 03 '23 at 13:17
  • yeah, definitely,the huygens principle is just an experimentally deduced geometrical construct,well i too am not satisfied learning just it,fenyman's path integral seems interesting,thank you for your suggestion,but can you answer the first part of my question? – Blz Nov 03 '23 at 17:09
  • I added some comments to waves cancelling here : https://physics.stackexchange.com/questions/23930/what-happens-to-the-energy-when-waves-perfectly-cancel-each-other/785200?noredirect=1#comment1765490_785200 – PhysicsDave Nov 03 '23 at 21:03
  • When we talk about light/photons you can get some important concepts in my recent answer here: https://physics.stackexchange.com/questions/784292/in-which-part-of-the-sagnac-fiber-optic-setup-will-the-light-undergo-the-most-in/784356?noredirect=1#comment1763413_784356 – PhysicsDave Nov 03 '23 at 21:05
  • wavelets reaching a point with similar quantities ?......its probably an assumption that was ok for 1700/1800s .... and the math works out very similarly to Feynman's integral ..... i.e. photons like to travel integer multiples of lambda/wavelength. – PhysicsDave Nov 03 '23 at 21:08
  • thanks alot @PhysicsDave – Blz Nov 04 '23 at 17:59

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