How to derive Intensity of light waves function I/Io

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The discussion focuses on deriving the equation I/Io = (I/N2)[(sin(NØ/2)/(sin(Ø/2))^2, where Ø is defined as (2πdsinΘ)/λ. Participants express difficulty in manipulating the equation and substituting Ø and d into it, often resulting in values of 1 or 0, which are not the desired outcomes. Clarification is sought regarding the meanings of I and I0, as well as the significance of the sine function in the equation. The connection to amplitude equations and trigonometric identities is also questioned, with an emphasis on understanding the derivation process. The conversation highlights the complexities of deriving light intensity ratios in wave functions.
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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?
 
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What is I and what is I0?
 
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.
 

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