# Homework Help: Derivation of the equation in doube slits

1. Aug 21, 2007

### Oerg

Hi, can someone provide me with a simple derivation of the formula: x=λD/a[/B]

2. Aug 21, 2007

### mgb_phys

Sorry - you have to do a bit more than that.
When you have tried to find an answer we can help!

3. Aug 22, 2007

### Oerg

oh boy! well... x=slit inteference, λ=wavelength of electromagnetic wave, D= distance between slit and board and a=difference in length of the 2 slits. I dun really know how to draw a diagram online so i will try my best to explain what im doing.

I would find through pythogaras theorem the difference in the distance to the exact same spot in the board from both slits and through an approaximation in binomial theorem, i arrived at (a^2+2ab)/D where b is the perpendicular distance from the horizontal of the slit to the point of inteference point of concern.

After which, calling the above difference in distance Y, i used a proportionality method which equated λ/Y=x/a.

but sadly i did not get the answer, it is quite vexing any help?

4. Aug 22, 2007

### mgb_phys

Because the angle is so small you can use x = sin x (x in radians) which helps with the derivation and then you are just trying to find the angle at which the difference in path is 1 wavelength.
I think you are over complicating it ! see here for diagram
http://www.matter.org.uk/schools/Content/Interference/formula.html [Broken]

Last edited by a moderator: May 3, 2017
5. Aug 22, 2007

### Astronuc

Staff Emeritus