Derivation of the equation in doube slits

[Oerg]

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

 

[mgb_phys]

Sorry - you have to do a bit more than that.
Start with explaining what the terms in the equation mean and draw a diagram for yourself - this will help you understand.
When you have tried to find an answer we can help!

 

[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 I am 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?

 

[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

 

[Astronuc]

Here's an alternative site with a good description of the double slit diffraction

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/slits.html