How to derive Intensity of light waves function I/Io

In summary, to derive the given equation I/Io= (I/N2)[(sinNØ/2)/(sinØ/2)]2, one can use the equation Ø= (2πdsinΘ)/λ and the relationship d=λ/sinΘ. The intensity ratio I/Io represents the number of slits, denoted by N, and the sin form is derived from the equation I=cA^2.
  • #1
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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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  • #2
What is I and what is I0?
 
  • #3
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.
 

Related to How to derive Intensity of light waves function I/Io

1. What is the formula for calculating the intensity of light waves?

The formula for calculating the intensity of light waves is I/Io = (E/Eo)^2, where I is the intensity of the light wave, Io is the initial intensity, E is the amplitude of the electric field, and Eo is the initial amplitude.

2. How do you derive the intensity of light waves function?

The intensity of light waves function can be derived using the formula I/Io = (E/Eo)^2. This formula is derived from the fact that the intensity of a wave is proportional to the square of its amplitude.

3. What is the significance of Io in the intensity of light waves function?

Io, or the initial intensity, is a reference point for measuring the change in intensity. It is the intensity of the wave at its starting point or initial position.

4. How does the amplitude of the electric field affect the intensity of light waves?

The intensity of light waves is directly proportional to the square of the amplitude of the electric field. This means that an increase in the electric field amplitude will result in a corresponding increase in the intensity of the light wave.

5. Can the intensity of light waves be negative?

No, the intensity of light waves cannot be negative. It is a measure of the amount of energy carried by the light wave and can only have positive values.

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