How Can Similar Triangles Help Prove Light Interference Formulas?

[MathematicalPhysicist]

i need to prove that sin(b_n)=(n*lambda)/d
while dX=(lambda*L)/d

this is a situation of monochromatic light inteference where dX is the is the distance between every adjacent light spots, lambda is ofcourse the light wavelength, L is the width between the two screens, d is the distance between the gaps of first screen and n describes the place of light spots.

i know it's rather simple but my text doesn't reveal all the simple algebraic and trigonometric tricks.
but i think that if we were to build a right triangle then n*dX equals one of its sides while L is the other and by pythogrean sentence the hypotenuse equals:
D=sqrt(L^2+n^2*(dX)^2)
and then sin(b_n)=(n*dX)/D
but this is as far as i went and i didn't get the formula i needed to prove, your input is appreciated.

 

[Astronuc]

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

Remember \theta ~ sin\theta ~ tan\theta for very small angles.