One slit diffraction: illustration using Huygens' principle, derivation for minima and examples.

in this video we're looking at one slit  diffraction for a light wave so on the left we have a bunch of parallel  wave fronts coming into this slit i've shown the slit as rather wide for purposes  of illustration and the key to understanding what's going on here is to use huygens principle and i'll post a link back to the video where we introduced huygens principle real quick huygens principle says that any wavefront can be represented as a bunch of superimposed point  sources so that's what i've shown inside the slit that little piece of the wavefront that survives  to pass through the slit can be represented as a bunch of little point sources stacked on each  other each of those emitting a circular wave in the forward direction so this creates this  whole interference pattern of semicircular waves each set of those concentric about  one of these little point sources well all those waves start to interfere and  where their crests align with each other and their troughs align with each other you end up with constructive interference where you have a mix of crests on top of troughs you end up with destructive interference and and in this diagram we only had enough space to  capture what's called the central maximum for the diffraction pattern so mathematically  that's represented by this red curve my maximum intensity is right along the center  line and then it dies off and i end up with a dead spot right here and a dead spot right  here now this pattern actually continues farther out into space and you'll get many many  diffraction maxima and minima off to the sides so what's going on here along the center line is  that if i look at all these little circular waves created by my point sources their crests are  overlapping crests almost perfectly on the center line the alignment starts to get off as i get away  from that center line so the intensity of light that i'm seeing is diminishing as i get away from  that center line by the time i get to these green lines this upper one here and the lower one here i  just have this terrible mix of wave crests sitting on top of troughs and vice versa and on average  i'm getting destructive interference and i get my so this blob on the  right is an actual photograph i took this morning of a diffraction pattern from passing red laser  light through a single slit it was so bright in it was so bright in the center that my phone just interpreted  it as white