Optics

Question 1

What is Snell’s Law?

Answer 1

n1sinθ1 = n2sinθ2

Question 2

What is the lens equation?

Answer 2

1 / u + 1 / v = 1 / f

Where:
* u is the object distance
* v is the image distance
* f is the focal length

(ur very fit)

Question 3

What are optical resonators, also known as optical cavities?

Answer 3

• An arrangement of mirrors (or other optical elements) that allows a beam of light

• to circulate in a closed path

• at certain resonant frequencies.

Question 4

What is the equation for the Q-factor of a gas laser cavity?

Answer 4

Q = f0 T(rt) (2π/L)

Where:
* f0 is the resonant frequency and
* f0 = c / λ

• T(rt) is the cavity round-trip time and
• T(rt) = 2L / c

Question 5

For particle sizes equal to or larger than a wavelength, ______ scattering predominates.

Answer 5

For particle sizes equal to or larger than a wavelength, (Mie) scattering predominates.

Question 6

Mie Scattering

______ interactions of ______ and ______ rays that result in ______ and ______ interference along different ______.

Answer 6

Mie Scattering

(Complex) interactions of (scattered) and (refracted) rays that result in (constructive) and (destructive) interference along different (paths).

Question 7

nλ = ?

Answer 7

nλ = dsinθ

Question 8

What constitutes a diffraction grating?

Answer 8

A large number of parallel, closely spaced slits.

Question 9

What is the resolving power of a diffraction grating?

Answer 9

R = λ / Δλ

Where Δλ is the smallest resolvable wavelength difference.

Question 10

______ is what happens with small holes and point light sources.

For example, _______.

Answer 10

(Interference) is what happens with small holes and point light sources.

For example, (Young’s Slits experiment)

Question 11

______ is what happens with finite and small holes and finite light sources.

For example, ______.

Answer 11

(Diffraction) is what happens with finite and small holes and finite light sources.

For example, (Single-slit, Fraunhofer diffraction)

Question 12

Give two examples of interference.

Answer 12

Young’s Slits experiment

Thin-film interference

Question 13

Give two examples of diffraction.

Answer 13

Single-slit (Fraunhofer) diffraction

Near-field (Fresnel) diffraction

Question 14

What is the equation for a travelling wave?

Answer 14

y(x, t) = A sin [kx - ωt + φ]

Where:
* A is the amplitude
* k is the wave number
* ω is the angular frequency
* φ is the phase

Question 15

Superposition of Waves

If φ = 0, _______ interference takes place. The waves ______ and have amplitude _____.

Answer 15

Superposition of Waves

If φ = 0, (constructive) interference takes place. The waves (add) and have amplitude (2A).

Question 16

Superposition of Waves

If φ = π, _______ interference takes place. The waves ______ and have amplitude _____.

Answer 16

Superposition of Waves

If φ = π, (destructive) interference takes place. The waves (cancel out) and have amplitude (zero).

Question 17

How is the Q-factor of a resonant optical cavity related to the resonant frequency (f0)?

Answer 17

Q = (2πf0) x (Energy Stored) / (Power Loss)

In other words, Q is the ratio of the stored energy to the energy dissipated per radian of the oscillation.

Where f0 is the resonant frequency.

Question 18

How is the Q-factor of resonant optical cavity related to the bandwidth (Δf)?

Answer 18

Q = f0 / Δf

Resonance bandwidth: the ratio of the resonance frequency f0 and the full width at half-maximum (FWHM) bandwidth Δf of the resonance.

Question 19

Describe what is meant by Rayleigh scattering.

Answer 19

Rayleigh scattering is the scattering of molecules to very tiny particles.

It favours very small wavelengths.

Question 20

Give an example of Rayleigh scattering.

Answer 20

The blue colour of the sky, since blue light is scattered slightly more efficiently than red.

You see light from Rayleigh scattering off the air.

Question 21

Briefly describe the differences between the cases of Fresnel and Fraunhofer diffraction.

Answer 21

Distance between slit, and source.

Fresnel:
- Finite distance from slit
- Cylindrical or spherical wavefront considered

Fraunhofer:
- Infinite distance from slit
- Plane wavefront considered

Question 22

What equation would you use to find the thickness of a film that is used to create constructive interference with a given value for the refractive index of the material and the wavelength of light?

Answer 22

2µt = (m + 1/2)λ

Where:
µ is the refractive index
t is the thickness
m is the order (1, 2, 3…)
λ is the wavelength

Question 23

What equation would you use to find the thickness of a film that is used to create destructive interference with a given value for the refractive index of the material and the wavelength of light?

Answer 23

2µt = (m)λ

Where:
µ is the refractive index
t is the thickness
m is the order (1, 2, 3…)
λ is the wavelength

Question 24

Describe what is meant by spatially coherent light.

Answer 24

Spatial coherence tells us how uniform the phase of the wave front is.

It is a measure of the correlation of a light wave’s phase at different points transverse to the direction of propagation.

Question 25

What is Brewster's angle?

Answer 25

tan(θb) = ne / n0 Where: θb = Brewster's angle (tilt angle to horizontal) ne = refractive index of second medium n0 = refractive index of first medium

Question 26

How would you find the thickness of a quarter-waveplate?

Answer 26

t(1/4) = (1/4) x (λ) / (ne - n0)

Question 27

How would you find the thickness of a half-waveplate?

Answer 27

t(1/2) = (1/2) x (λ) / (ne - n0)

Question 28

How does subtractive colour work?

Answer 28

Subtractive primaries relfect two of the RGB. This means that only one of the RGB is absorbed.

Question 29

How does additive colour work?

Answer 29

Additive primaries relfect one of the RGB. This means that two of the RGB are absorbed.

Question 30

Additive Colour System Red + Green = ?

Answer 30

Additive Colour System Red + Green = Yellow

Question 31

Additive Colour System Red + Blue = ?

Answer 31

Additive Colour System Red + Blue = Magenta

Question 32

Additive Colour System Blue + Green = ?

Answer 32

Additive Colour System Blue + Green = Cyan

Question 33

Give the equation for angular magnification for a telescope.

Answer 33

M = -fo / fe Where: fo is the focal length of the objective lens fe is the focal length of the eyepiece

Question 34

What is the wavelength of red light?

Answer 34

λ(red) ~ 650nm

Question 35

What is the wavelength of green light?

Answer 35

λ(green) ~510nm

Question 36

What is the wavelength of blue light?

Answer 36

λ(blue) ~450nm

Question 37

How do you find the critical angle?

Answer 37

sin(θc) = ne / n0

Question 38

How would you find the coherence time for a given frequency bandwidth?

Answer 38

t(c) = 1/f

Question 39

How do you find the coherence length of a laser beam?

Answer 39

L = c t(c) Where: L is the coherence length c is the speed of light t(c) is the coherence time

Question 40

How would you find the position (distance from central fringe) of a maximum for Young's Double Slit experiment?

Answer 40

y = mλD/d Where: m is the order λ is the wavelength of light D is the distance between the slits and the screen d is the slit distance

Question 41

Describe briefly what is meant by Fresnel diffraction.

Answer 41

Fresnel diffraction is a “near-field” phenomenon, which occurs when the usual approximations used for Fraunhofer diffractions, such as: * parallel rays from a point-source * the screen distance being > > aperture size and > > λ no longer hold.

Question 42

Describe what is meant by temporal coherent light.

Answer 42

Temporal coherence is a measure of the average correlation between • the value of a wave and • itself delayed by τ at any pair of times

Question 43

How would you find the angle of a first order diffraction with an angle of incidence?

Answer 43

nλ = d(sinθ - sinθi)

Question 44

What does NA stand for?

Answer 44

Numerical Aperature

Question 45

What is the formula for NA?

Answer 45

NA = n sinθ

Question 46

What is the equation for microscopic resolution?

Answer 46

Δx = λ / 2(NA)

Question 47

What should you assume the wavelength of light is?

Answer 47

550nm

Question 48

How do you calculate birefringence?

Answer 48

ne - n0

Question 49

Why do most optical fibre telecoms systems operate in the infra-red part of the EM spectrum?

Answer 49

* Rayleigh scattering is an important component of the scattering of optical signals in optical fibres * Silica fibres are disordered materials, thus their density varies on a microscopic scale * The density fluctuations give rise to energy loss due to the scattered light

Question 50

Describe a common practical application for the phenomenon of polarisation by reflection.

Answer 50

Polarized sunglasses use the Brewster's angle to eliminate glare from the sun. In a large range of angles around Brewster's angle, the reflection of p-polarized light is lower than s-polarized light.

Question 51

Describe how the diameter (aperture) of a telescope is a critical parameter when considering the capabilities of the instrument.

Answer 51

The aperture of a telescope refers to the objective lens. A larger objective lens creates a larger magnification. Whilst high magnification makes an object appear larger, light gathered by the scope is spread over a larger area creating a fainter image

Question 52

What is Malus' Law?

Answer 52

I(θ) = I(0) cos^2θ Where: I(0) is the initial intensity I(θ) is the intensity due to the angle

Question 53

What is normal dispersion?

Answer 53

It is generally obsereved that the refractive index decreases with increasing wavelength. This is called normal dispersion.

Question 54

What is anomalous dispersion?

Answer 54

In the small wavelength ranges, there is often increase of refractive index with increase of wavelength, due to absorption of radiation. This is called anomalous dispersion.

Question 55

What is the Rayleigh criterion for a circular aperture?

Answer 55

sinθ = 1.22λ / D Where: θ is the angular resolution (radians) λ is the wavelength of light D is the diameter of aperture

Question 56

What is the Rayleigh criterion for a single slit?

Answer 56

sinθ = λ / D Where: θ is the angular resolution (radians) λ is the wavelength of light D is the diameter of aperture