How to derive Intensity of light waves function I/Io

[fva65]

Homework Statement

How do you derive the following equation given I/Io= (I/N²)[(sinNØ/2)/(sinØ/2)]²

given that Ø= (2πdsinΘ)/λ

Homework Equations

Ø= (2πdsinΘ)/λ

d=λ/sinΘ

The Attempt at a Solution

I have tried substituting Ø into the equation as well as d=λ/sinΘ, but I always seem to make the equation equal to 1 or 0 and this really isn't what I'm looking for. Does this equation come from an amplitude equation using trig identities of some sort?

 

[Gear300]

What is I and what is I₀?

 

[fva65]

I/Io is the intensity ratio and N is equivalent to the number of slits where minimum N=2 but I'm stuck from there. I'm not sure where the sin form comes from. I'm thinking it may come from the equation I=cA^2 but I'm not sure.