Double Slit Diffraction Problem

[spitonem]

I had this problem on my exam and I was pretty sure i knew what to do but it couldn't come up with the right answers.
I diagrammed the problem and showed the way i tried to solve it in blue. Can someone tell me where i went wrong?

Basically i found the length the of the first maximum off the center. i used Pythagorean's theorem to find D2. Then subtracted the two distances to find the difference. I then took the arctan of that distance divided by D1.

 

[Simon Bridge]

You way over-thought the problem.
Start from the physics: what is the condition that makes a maximum?

 

[spitonem]

the center of a maximum is complete constructive interference from two rays of light?

 

[Simon Bridge]

the center of a maximum is complete constructive interference from two rays of light?

... good - so what is the condition for constructive interference in terms of the path lengths?

 

[spitonem]

wouldn't it be the wavelength plus by any integer being multiplied by the wavelength?

 

[Simon Bridge]

wouldn't it be the wavelength plus by any integer being multiplied by the wavelength?

Almost: the path difference has to be a whole number of wavelengths for constructive interference.
This makes the central maximum the zeroth maximum ... with the 1st and second etc on either side of it.

Lets say D is the perpendicular distance from the slits to the screen - as it is in your diagram.
If D>>d, the path difference between the zeroth maximum and the nth maximum is $D_n-D=d\sin\theta_n$
You've seen a formula like that before.