- #1

Aurelius120

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- 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

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}##?

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)