5 Slit Experimen: Probability Distribution Function

[zheng89120]

1. Homework Statement [/b]

given the following probability distribution function from 5 slits (y is verticle on screen)

P(y) = A | $$\sum$$(from n=-2 to 2) exp(ikR(n)) |^2

where k = 2$$\pi$$/$$\lambda$$

and R(n) ~ $$\approx$$ R-nyD/L

Show that the probability distribution as a function of angle from normal is:

P(theta) = |A|^2 |2 cos(2b[theta]) + 2 cos(b[theta]) + 1|^2

What is b??

2. Relevant equation

[theta] = y/L

Complex numers, Euler's equation

3. The Attempt at a Solution

I expanded out the equation with k and R$$_{n}$$ plugged in - got a bunch of cos's and i*sin's. Too much to type...

 

[zheng89120]

A wrote out the exp(ikR(n)) 's, and crossed multiplied 5 terms by 5 terms...

may get an answer soon?