# Double slit experiment wavelength

1. May 9, 2010

### fluidistic

1. The problem statement, all variables and given/known data
A extent ray of light with wavelength $$\lambda _0=632.8 nm$$ incide over a screen containing 2 horizontal parallel slits very thin and separated by a distance of 0.2 mm. We observe an interferance over a screen at 1.00 meter away from the screen containing the horizontal slits.
1)At what distance from the principal axis are situated the first zeros of irradiance?
2)How far from the principal axis is the fifth bright fringe?
3)Compare the previous results.

2. Relevant equations
I know I should find the formula given there: http://en.wikipedia.org/wiki/Double-slit_experiment#Results_observed but how to reach this?

3. The attempt at a solution
3) Since I already made the experiment, I know that the fifth fringe is roughly 5 times farer than the 1st fringe, from the principal axis. Hmm not sure it's true, but I know that the distance between the fringes is equal. So my statement is true only if the first fringe coincide with the principal axis, which isn't true.
1)Irradiance is the Poynting vector averaged over... well I'm not sure. It's worth $$\frac{|\vec E_0 |^2}{2 \eta}$$ according to my notes. So I need to find out the electric field of the wave.
I know that there are 2 sources of light considering the problem after the light from the laser passed by the slits. How are these waves? Cylindrical? I never dealt with such waevs. Spherical? Can I consider them as plane waves since the 1 meter distance is really big compared to the wavelength of the wave? In that case E total is the sum of $$E_1= E_0 \cos (kx - \omega t + \alpha)$$ and $$E_2= E_0 \cos (k... - \omega t + \alpha)$$. Can you help me with the "..." part? I don't know what to put as "x".

Also I don't know how can L=1m appear in the final result. I guess I should consider the wave as cylindrical, but I've no idea about how the expression is.
Any idea?

2. May 10, 2010

### nickjer

I don't understand a lot of what you are saying. But if all you need to do is find the double slit interference equation then all you need to do is find the path length difference between the two waves originating from both slits to the wall, $\Delta L$. If the path length difference is $m\lambda$ then you have constructive interference assuming both waves are in phase.