Young's Slits Derivation

Derivation of formula for Youngs slits:

D₁² = D² + (y-d/2)² = D² + y²-yd + d²/4 

and obviously

D₂² = D² + (y+d/2)² = D² + y²+yd + d²/4 

subtracting..

D₁² - D₂² = 2yd 

so

(D₁- D₂)(D₁+ D₂) = 2yd 

but

D₁+ D₂ ~ 2D

and for constructive interference

D₁- D₂ = nλ

giving

y = nλ D       
     d 

or (since y ~ D sin(θ) ~ Dθ)

d sin(θ) = nλ

or

θ = nλ
    d