Interference and Resolution

Question 1

What does coherence mean?

Answer 1

WHen two wave sources are at the same frequency and have a constant phase difference.

Question 2

Describe the thin film interference.

Answer 2

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.

Question 3

When does constructive interference occur in the thin film situation?

Answer 3

If the reflection from the lower surface ofthe thin film is in phase with the reflection from the upper surface of the thin film.

Question 4

If n3>n2>n1, when will constructive interference occur?

Answer 4

If the path length through the thin film isequal to an integer number of wavelength.

Question 5

If n3>n2>n1, whenwill destructive interference occur?

Answer 5

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)

Question 6

For 2 coherent light sources, what can we assume if D&raquo_space; d.

Answer 6

That the angle to P from each light source is equal to theta.

Question 7

What is the phase of each point source at point P?

Answer 7

Point 1: φ1 = kx1 - ωt

Point 2: φ2 = kx2 - ωt = φ1 + dφ

Question 8

What is the distance from each point source to point P?

Answer 8

Point 1 to P: x1

Point 2 to P: x1 + dx = x1 + dsin(theta)

Question 9

What is the equation for the wave at point P due to both sources?

Answer 9

e^(iφ1)*(1+e^(idφ))

Question 10

What is the equation for intensity at point P

Answer 10

Intensity is proportional to 2*(1+cos(kd sin(theta))

Question 11

When does constructive interference occur?

Answer 11

When kd sin(theta) = 0 or 2pi x integer.

Question 12

When does destructive interference occur?

Answer 12

When kd sin(theta) = pi + 2pi x integer

Question 13

What is an alternative approach to the two point source interference problem?

Answer 13

Using a phasor diagram.

Question 14

What is intensity proportional to on the phasor diagram?

Answer 14

2(1+cos(Δφ))

Question 15

What is the complex equation for multiple point sources?

Answer 15

e^(iΔφ)*(1+e^(iΔφ)+e^(i2Δφ)+…), where Δφ = kdsin(theta)

Question 16

How can you represent multiple point sources of a phasor diagram?

Answer 16

start with Δφ and keep increasing, making the start of a circle shape.

Question 17

When do you get central maximums, and the following minimums and maximums?

Answer 17

Central maximum: Δφ = 0, theta = 0
First minimum: nΔφ = 2pi
Next maximum: nΔφ = 3pi

Question 18

How do you solve the intensity for each minimum/maximum on the phasor diagram>

Answer 18

The points lie on the arc of a circle with centre Q.

Question 19

What is the equation for intensity of the minimums and maximums?

Answer 19

Intensity = I0*(sin^2(nΔφ/2))/(sin^2(Δφ/2))

Question 20

How can you check this intensity equation?

Answer 20

Set n=integer and see if the answer makes sense.

Question 21

How does multiple slit interference link with single slit diffraction?

Answer 21

You can think of little points in the slit as individual point sources, which is the same as multiple sources.

Question 22

How does the phasor diagram differ for the single slit diffraction?

Answer 22

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.

Question 23

What is the intensity of a point in single slit diffraction?

Answer 23

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.

Question 24

What does the phasor diagram look like for the single slit?

Answer 24

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.

Question 25

What happens to the central maximum when you narrow the slit?

Answer 25

The central maximum becomes broader.

Question 26

What is the equation for intensity of multiple slits of finite width?

Answer 26

I = I0sinc^2(beta/2)/(sin^2(nΔφ/2))/(sin^2(Δφ/2)), where beta = ka sin(theta) and Δφ = kd sin(theta)

Question 27

What is a diffraction grating?

Answer 27

A diffraction grating has a large number of slits.

Question 28

What is the equation for maxima of diffraction gratings?

Answer 28

dsin(theta)=nλ

Question 29

What is an airy disc and how does it determine resolution?

Answer 29

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.