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Interference and Diffraction (Relationships (Slit size(a) (This is the…
Interference and Diffraction
Relationships
Slit size(a)
This is the easiest to visualize
Thin width
Imagine the width being small enough where it acts as a singular circular point source
Thin causes the diffraction pattern to stretch
A wider slit width causes the pattern to shrink
Wide width
Imagine the width being fairly wide
In this case the planar wave would just continue moving through
Slit separation(d)
Wavelength(\(\lambda\))
\(dsin\theta=m\lambda\)
\(\lambda\) is proportional to \(\theta\)
\(\lambda\) is inversely proportional to frequency(f)
This means that frequency for a larger wavelength like red has low frequency
If we had a fast frequency like violet(380nm for \(\lambda\)) for 2 slits we can imagine more points interfering
Combining Interference and Diffraction
Diffraction's influence
Proof
Single Slit
Envelope
!
The slit width sets a restriction on the intensity
On the graph this means for any number of slits we're limited to the envelope
On the pattern this means that we'd see the same spread for the multiple slits
Changing slit width
It stretches the pattern
Missing maxima
Interference's Influence
We're always limited to the envelope caused by the diffraction(finite slit width)
Changing number of slits(N)
This changes where the minimums are
\(\Delta D_{adj}=dsin\theta=\frac{\lambda}{N}\)
The path difference between adjacent slits is equal to the wavelength over the number of slits
This equation is for finding interference minimums
Anytime the result is a multiple of \(\lambda\) it is constructive interference, otherwise it's destructive
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Changing separation of slits(d)
\(dsin\theta=m\lambda\) constructive interference
d and sin\(\theta\) are inversely proportional
If d increases \(sin\theta\) decreases
\(\theta\) represents the angle from the center maximum to a min or max
If the \(\theta\) for each constructive interference decreases it means that distance between each max and min compared to the central max decreases
This causes more peaks within the envelope
