Young's double slit experiment (prob density)

Hootenanny

HINT:

[tex]\cos^2\theta = \frac{1}{2}\left(1+\cos\left(2\theta\right)\right) \Rightarrow \frac{1}{2}\left(1+\cos\left(\theta\right)\right) = \cos^2\left(\frac{\theta}{2}\right)[/tex]

t_n_p

Got it! Thanks a WHOLE lot!

There's another follow on question..
Show that interference maxima is given by


Ignoring part c) for the time being, how exactly is pr density related to the interference maxima equation?

Hootenanny

Check out the slit interference pages at hyperphysics: http://hyperphysics.phy-astr.gsu.edu...opt/slits.html

t_n_p

hmmm, still don't get it.

Hootenanny

What specifically don't you understand?

t_n_p

how the prob density equation just found is related to the interference equation.

Hootenanny

There's no need to relate the probability density to the interference pattern, the question simply asks you to derive the fringe separation, which can be done without using the probability density.

t_n_p

hmm? It says "Using the results obtained in (a) [The pr density part], show that the interference maxima are given by..."

Hootenanny

Okay, how does the maxima relate to [itex]\rho[/itex]? What is a maxima?

t_n_p

So derive [itex]\rho[/itex] in terms of [itex]\psi[/itex] and set to zero?
What about A (imaginary number?)

t_n_p

Also, where would lambda come from?

Hootenanny

Who would one set [itex]\rho[/itex] to zero? Wouldn't a maxima occur when [itex]\rho[/itex] is greatest?
What is the maximum value of [itex]\rho[/itex]?

t_n_p

The maximum value of [itex]\rho[/itex] is 1, or at least that is what I think. But where to from there?

Hootenanny

No it isn't

t_n_p

infinity????

Hootenanny

What is the maximum value of [itex]\cos^2\theta[/itex]?

t_n_p

1!!!!!!!!