00:01
All right, so let's say we have a double slit interference pattern, this is problem a, where our slits are separated by a distance of 0 .53 millimeters.
00:11
And we want to find the sort of angular locations of the first and second maximum, using a wavelength of 580 nanometers.
00:24
So our equation for interference, constructive interference, is like d times the sign of theta n equals n lambda so theta one if we solve for this is going to be like the inverse sign of lambda over d and then theta two is going to be the inverse sign of twice that argument sorry i didn't mean to put a two there inverse sign of two lambda over d and so if we plug in our values for each of these uh theta two comes out to about 0 .125 degrees and then theta 1 is about 0 .06 to 7 degrees.
01:05
They're nearly separated by a factor 2 as well.
01:09
So that's part a.
01:11
And part b says, now suppose these slits are separated by 0 .32 millimeters, what is the intensity at these two locations, at these two angles that we're talking about? so the intensity as a function of what's some parameter we'll call alpha is going to be i -0.
01:32
Like the initial intensity times the sign of alpha over alpha squared.
01:39
And alpha is going to be pi times d times the sine of theta over lambda.
01:49
So that's our parameter we're using.
01:52
And so we'll have like an alpha one and an alpha two to plug in...