Plotting I/Io vs Phi: 3-Slit System w/650 nm Wavelength

[Evaaa]

Homework Statement

A three slit system is illuminated by light with a wavelength of 650 nm. The slits are evenly spaced with a slit space of 1.28 mm and a slit width of 0.16 mm

A) Using Excel, plot the modulated interference pattern for +or - 0.5° or so. Plot I/Io.
b) Are there any missing orders?
c) Draw a phasor diagram for the second minima from the center of the interference pattern.

Homework Equations

im not really sure which equations to use, but i assume i should use:
I= Io[(sin²(N*phi/2)/(sin²(phi/2)]
phi=[ (2*pi)/ lamda ] * d*sin(theta)
?

The Attempt at a Solution

I figured N would equal 3 because there is three slits.
and phi would equal 256.4 after plugging in all the values (+0.5 degrees).
but i have no clue how to find Io or how to plot the graph.

i know that i have to plot I/Io vs phi, and that at phi equal to 0, i have a maximum bright fringe that should be 9Io, and then at phi equal to pi i have another bright fringe (but its intensity is Io) an then at phi equal to 2pi i have another maxmimum bright fringe.

help?

 

[anathema]

I can help you with this problem. Let's break it down step by step:

Step 1: Finding Io
To find Io, we need to use the equation for the intensity of light in a double-slit interference pattern:

I = Io(sin(θ/2)/ (θ/2))^2

Since we are given a three-slit system, we need to multiply this equation by 3 to account for the three slits. So our final equation for Io becomes:

Io = 3I/(sin(θ/2)/ (θ/2))^2

To find Io, we need to plug in the values given in the problem:

λ = 650 nm
d = 1.28 mm
w = 0.16 mm

We also need to convert the slit width from mm to meters, so w = 0.16 mm = 0.00016 m.

Now we can plug these values into our equation for Io:

Io = 3I/(sin((2πd/λ)sin(θ/2)/ (θ/2))^2

Io = 3I/(sin((2π*0.00128 m)/(0.00065 m)sin(θ/2)/ (θ/2))^2

Io = 9I/(sin(0.00394θ/2)/ (0.00394θ/2))^2

Io = 9I/(sin(0.00197θ)/ (0.00197θ))^2

Io = 9I/((0.00197θ)^2/sin^2(0.00197θ))

Now, we can use this equation to find the value of Io for a given value of θ. For example, if we want to find the intensity at θ = 0, we can plug in θ = 0 into our equation:

Io = 9I/((0.00197*0)^2/sin^2(0.00197*0))

Io = 9I/((0)^2/0)

Since we cannot divide by 0, this means that Io is undefined at θ = 0. This makes sense because at θ = 0, we have a maximum bright fringe, so the intensity is at its maximum value.

Step 2: Plotting the Modulated Interference Pattern
To plot the mod