OP: Diffraction, Wave Optics, Coherence - Week 4

Question 1

What is the corpuscular theory of light?

Answer 1

A.K.A particle theory of light.

states that light is made up of small discrete particles called ‘corpuscles” (little particles) which travel in a straight line with a finite velocity and possess impetus/energy

Question 2

How did Newton describe the travelling of particles of light?

Answer 2

As travelling through a medium of an invisible aether

Question 3

How did Newton’s particle model explain reflection?

Answer 3

the corpuscles bounce of the boundary, with their vertical velocity reversed and horizontal velocity unchanged

Question 4

How did Newton’s particle model explain refraction?

Answer 4

he argues that the corpuscles traveled faster in the glass so that their vertical velocity was accelerated by some attractive force exerted on the corpuscles by the medium

He also said that particle size differed with colour, and therefore refract differently, to explain the light spectrum

Question 5

Why did people accept Newton’s particle theory?

Answer 5

Because nobody at the time could measure the speed of light in a medium

• and he was a famous genius

Question 6

Who came up with the wave model of light? But in what way did he describe the waves that differs to today’s understanding?

Answer 6

Cristiaan Huygens. But he said the waves were longitudinal, rather than our current understanding that they are transverse

Question 7

How did Huygens describe the speed of waves when travelling from air to a denser material

Answer 7

He said that the waves slow down! (contradicting Newton’s idea that particles sped up)

Question 8

In Huygens’ model, what is significant about each point on a wavefront?

Answer 8

Each point along a wavefront is the source for new ‘wavelets’, i.e. each point is a source of circular (hemi-spherical) waves

Question 9

Which theory better explains interference patterns (newton’s rings)? Newton or Huygen?

Answer 9

Huygen’s wave theory

Question 10

How does diffraction work?

Answer 10

It is the phenomenon where light energy spreads out as it travels through an aperture. (or bends around a corner as it travels through)

Question 11

When diffracted light impinges on a screen, what is the result?
(- i.e. when diffracted wave comes through a single slit/hole/aperture)

Answer 11

A pattern of maxima and minima is formed. (i.e. a pattern of light and dark bands).

The pattern is called “Airy’s disk”, when in 2-dimensions

Question 12

When light passes through an aperture and diffracts, in what region is the light brightest?

Answer 12

At the centre of the aperture/airy disk

Question 13

How does the size of the aperture affect the level of diffraction?

Answer 13

Effect of diffraction is much larger with smaller aperture size

Question 14

Explain the basis behind Thomas Young’s 2-slit experiment

Answer 14

He theorised, based on sound waves interference, that light waves could also interfere with each other. So he passes light through 2 nearby apertures

Question 15

What determines the way in which waves interfere?

Answer 15

Amplitude and Phases (assuming frequencies and wavelengths are equal)

Question 16

How do you obtain Constructive vs Destructive interference?

Answer 16

Constructive: waves in-phase
Destructive: waves out-of-phase

Question 17

What is (spatial) Coherence?

Answer 17

The degree to which the local phase of a wave can be predicted from watching other waves nearby at the same time

Question 18

What is (temporal) Coherence?

Answer 18

The degree to which the local phase of a wave can be predicted by observing what has happened locally in the immediate past

Question 19

How does coherence influence the ability of light passing through 2 slits to form an interference pattern?

Answer 19

Coherent = interference pattern is formed (with alternating bright and dark spots)
Non-coherent = NO interference pattern

Question 20

Are you able to get interference from 2 independent emitters of light?

Answer 20

NO

Question 21

When light is passing through 2 slits, when will we see constructive interference?

Answer 21

When the distance between each slit and the image location point is the same or differ by exactly ‘m’ wavelength (m = 1, 2, 3 etc.)

Question 22

Where will the dark fringes of light appear in an interference pattern?

Answer 22

Appear where you have ‘destructive’ interference.

- i.e. when one wave is 180deg out of pahse with the other

Question 23

Do you still get an interference pattern when you turn down intensity and only one photon reaches the 2 slits at one time? If so, why?

Answer 23

YES, because the particles have an inherent wave-like nature

Explained by Heisenberg’s Uncertainty Principle - you can’t simultaneously know both a particle’s position and velocity at the same time

Question 24

What happens when you pass a laser beam through a very small aperture?

Answer 24

You get an interference pattern (Airy’s Disk)

Question 25

Is it possible to achieve point-to-point imagery?

Answer 25

NO. No matter how small the object. This is because it is prevented by diffraction (so the wave-like nature of light).

• best you can achieve is blob-to-blob imagery

Question 26

Describe the brightness pattern of an Airy Disk

Answer 26

The bands of light and dark start of brighter and get progressively dimmer as you go outwards towards the periphery of the disk

Question 27

Describe the formula that relates aperture diameter, to the angle of the aperture and to the wavelength of the light?

Answer 27

Dsin(theta) = 1.22lambda

Theta = the angle of the aperture subtended by the middle of the airy disk and it’s first minima

D = aperture diameter

theta = 1.22lambda/D

Question 28

Explain Rayleigh’s criteria

Answer 28

The smallest angular separation of things that we can image in a system is limited by diffraction when the peak of one point lands on the minima of the airy disk produced by a neighbouring point

• i.e. two point sources separated by less than the radius of Airy’s disk cannot be resolved/distinguished from each other

Question 29

For a natural pupil size (5mm) and light in the middle of the visible spectrum (500nm), is visual acuity limited by Diffraction? Explain.

Answer 29

No.
For 6/3 V.A: limbs separated by 0.146mrad can be resolved
Rayleigh’s criterion: 0.122mrad in this case (theta = 1.22x5x10^-5cm/0.5cm)

0.146 is greater than 0.122. So 6/3 can be resolved (ideally).

Question 30

For a small pupil size (2.5mm) and light in the middle of the visible spectrum (500nm), is visual acuity limited by Diffraction? Explain.

Answer 30

Yes.
For 6/3 V.A: limbs separated by 0.146mrad can be resolved
Rayleigh’s criterion: 0.244mrad in this case (theta = 1.22x5x10^-5cm/0.25cm)

0.146 is less than 0.244. So 6/3 cannot be resolved.

Question 31

What is the goal of laser interferometry? How does it work?

Answer 31

Goal: to make an interference pattern happen on the retina itself

since laser light has a long coherence “length”, the 2 beams can interfere with each other, giving rise to a grating pattern on the retina

Question 32

How can laser inferometry be used clincally?

Answer 32

Can be used as a “Potential Acuity Meter” to assess the potential visiual acuity that a person with optical problems such as cataract or keratoconus might achieve after surgery

Question 33

How does rayleigh’s criterion relate to reading DVDs, CDs etc?

Answer 33

The formula theta = 1.22lmabda/d is important for detecting the microscopic features such as the little pits that encode data on CDs, DVDs etc.

Question 34

Is microscopic resolution limited by rayleigh’s criterion?

Answer 34

Yes

Question 35

Describe our current understanding on how light operates

Answer 35

Photons are particles that behave as waves