Interference and Resolution Flashcards
What does coherence mean?
WHen two wave sources are at the same frequency and have a constant phase difference.
Describe the thin film interference.
2 boundaries: air to thin film and thin film to glass. Light is incident on the film and some is reflected at the film and some is reflected from the glass.
When does constructive interference occur in the thin film situation?
If the reflection from the lower surface ofthe thin film is in phase with the reflection from the upper surface of the thin film.
If n3>n2>n1, when will constructive interference occur?
If the path length through the thin film isequal to an integer number of wavelength.
If n3>n2>n1, whenwill destructive interference occur?
If the reflection from the lower surface of the thin film leaves exactly out of phase as the reflection from the upper surface (2t = (m+1/2)lambda)
For 2 coherent light sources, what can we assume if D»_space; d.
That the angle to P from each light source is equal to theta.
What is the phase of each point source at point P?
Point 1: φ1 = kx1 - ωt
Point 2: φ2 = kx2 - ωt = φ1 + dφ
What is the distance from each point source to point P?
Point 1 to P: x1
Point 2 to P: x1 + dx = x1 + dsin(theta)
What is the equation for the wave at point P due to both sources?
e^(iφ1)*(1+e^(idφ))
What is the equation for intensity at point P
Intensity is proportional to 2*(1+cos(kd sin(theta))
When does constructive interference occur?
When kd sin(theta) = 0 or 2pi x integer.
When does destructive interference occur?
When kd sin(theta) = pi + 2pi x integer
What is an alternative approach to the two point source interference problem?
Using a phasor diagram.
What is intensity proportional to on the phasor diagram?
2(1+cos(Δφ))
What is the complex equation for multiple point sources?
e^(iΔφ)*(1+e^(iΔφ)+e^(i2Δφ)+…), where Δφ = kdsin(theta)
How can you represent multiple point sources of a phasor diagram?
start with Δφ and keep increasing, making the start of a circle shape.
When do you get central maximums, and the following minimums and maximums?
Central maximum: Δφ = 0, theta = 0
First minimum: nΔφ = 2pi
Next maximum: nΔφ = 3pi
How do you solve the intensity for each minimum/maximum on the phasor diagram>
The points lie on the arc of a circle with centre Q.
What is the equation for intensity of the minimums and maximums?
Intensity = I0*(sin^2(nΔφ/2))/(sin^2(Δφ/2))
How can you check this intensity equation?
Set n=integer and see if the answer makes sense.
How does multiple slit interference link with single slit diffraction?
You can think of little points in the slit as individual point sources, which is the same as multiple sources.
How does the phasor diagram differ for the single slit diffraction?
We need to consider more sections as we do not know how many point sources there are - in the end it will be a continuous arc.
What is the intensity of a point in single slit diffraction?
I = I0*(sin(beta/2)/(beta/2))^2 = I0 sinc^2(beta/2), where I0 is the intensity at the slit and beta = kasin(theta) where a is the slit width.
What does the phasor diagram look like for the single slit?
The start of a circle with a line from 0 to the final point T, and the circle centre is Q, with beta/2 as the length between Q and m, the centre point of the line between O and T.
What happens to the central maximum when you narrow the slit?
The central maximum becomes broader.
What is the equation for intensity of multiple slits of finite width?
I = I0sinc^2(beta/2)/(sin^2(nΔφ/2))/(sin^2(Δφ/2)), where beta = ka sin(theta) and Δφ = kd sin(theta)
What is a diffraction grating?
A diffraction grating has a large number of slits.
What is the equation for maxima of diffraction gratings?
dsin(theta)=nλ
What is an airy disc and how does it determine resolution?
Diffraction from circular apertures creates an Airy disk diffraction pattern. Two objects will be resolved when the first maxima of one object is in the first minima of the other.
