by Salvadoramerican » Wed Apr 11, 2012 8:04 am
sure first of lets begin with the fundamental two-slit formula [unparseable or potentially dangerous latex formula] anf the single slit [unparseable or potentially dangerous latex formula] its gonna get confusing so bear with me first lets start of with the dark fringes
The first dark fringes for diffraction are located at [unparseable or potentially dangerous latex formula]then [unparseable or potentially dangerous latex formula] where Y is their distance from the center of the central diffraction maximum, x is the distance of the two slits from the screen which reflects the interference pattern, l is the wavelength, and a is the width of the slits. Since these diffraction minima occur on either side of the diffraction central maximum, we have the total distance between them equal to [unparseable or potentially dangerous latex formula]
The interference maxima are given by [unparseable or potentially dangerous latex formula]
The number of maxima inside a given width [unparseable or potentially dangerous latex formula] centered on the central maximum for interference (which coincides with the central maximum for diffraction) is [unparseable or potentially dangerous latex formula] with [unparseable or potentially dangerous latex formula]. being the largest value of m for which the interference maximum still fits inside [unparseable or potentially dangerous latex formula]. This occurs since we have [unparseable or potentially dangerous latex formula]. interference maxima on either side of the central maximum then [unparseable or potentially dangerous latex formula]
then we substitute y with an equation above thus [unparseable or potentially dangerous latex formula]
where we note the strictly less than sign results since a maximum that occurs right at the diffraction minimum would not appear. Since [unparseable or potentially dangerous latex formula]. must be an integer, we have [unparseable or potentially dangerous latex formula]
then finally with nearest integer meaning the nearest integer smaller than or equal to the quantity in the square bracket. Hence the number of maxima is
[unparseable or potentially dangerous latex formula]
wow thats was longer than i thought
Last edited by
Salvadoramerican on Thu Apr 12, 2012 7:33 am, edited 1 time in total.
MacArthur HS-Irving
Region 1 5A
Officially retire: It was an honor to compete against Dominic Yurk and his school, Paschal High(I attended Freshmen year there), in Science, gave a good fight.
It was a pleasure to compete with everyone in math thanks guys