Optics Flashcards
What is Snell’s Law?
n1sinθ1 = n2sinθ2
What is the lens equation?
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)
What are optical resonators, also known as optical cavities?
• An arrangement of mirrors (or other optical elements) that allows a beam of light
• to circulate in a closed path
• at certain resonant frequencies.
What is the equation for the Q-factor of a gas laser cavity?
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
For particle sizes equal to or larger than a wavelength, ______ scattering predominates.
For particle sizes equal to or larger than a wavelength, (Mie) scattering predominates.
Mie Scattering
______ interactions of ______ and ______ rays that result in ______ and ______ interference along different ______.
Mie Scattering
(Complex) interactions of (scattered) and (refracted) rays that result in (constructive) and (destructive) interference along different (paths).
nλ = ?
nλ = dsinθ
What constitutes a diffraction grating?
A large number of parallel, closely spaced slits.
What is the resolving power of a diffraction grating?
R = λ / Δλ
Where Δλ is the smallest resolvable wavelength difference.
______ is what happens with small holes and point light sources.
For example, _______.
(Interference) is what happens with small holes and point light sources.
For example, (Young’s Slits experiment)
______ is what happens with finite and small holes and finite light sources.
For example, ______.
(Diffraction) is what happens with finite and small holes and finite light sources.
For example, (Single-slit, Fraunhofer diffraction)
Give two examples of interference.
Young’s Slits experiment
Thin-film interference
Give two examples of diffraction.
Single-slit (Fraunhofer) diffraction
Near-field (Fresnel) diffraction
What is the equation for a travelling wave?
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
Superposition of Waves
If φ = 0, _______ interference takes place. The waves ______ and have amplitude _____.
Superposition of Waves
If φ = 0, (constructive) interference takes place. The waves (add) and have amplitude (2A).
Superposition of Waves
If φ = π, _______ interference takes place. The waves ______ and have amplitude _____.
Superposition of Waves
If φ = π, (destructive) interference takes place. The waves (cancel out) and have amplitude (zero).
How is the Q-factor of a resonant optical cavity related to the resonant frequency (f0)?
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.
How is the Q-factor of resonant optical cavity related to the bandwidth (Δf)?
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.
Describe what is meant by Rayleigh scattering.
Rayleigh scattering is the scattering of molecules to very tiny particles.
It favours very small wavelengths.
Give an example of Rayleigh scattering.
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.
Briefly describe the differences between the cases of Fresnel and Fraunhofer diffraction.
Distance between slit, and source.
Fresnel:
- Finite distance from slit
- Cylindrical or spherical wavefront considered
Fraunhofer:
- Infinite distance from slit
- Plane wavefront considered
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?
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
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?
2µt = (m)λ
Where:
µ is the refractive index
t is the thickness
m is the order (1, 2, 3…)
λ is the wavelength
Describe what is meant by spatially coherent light.
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.
What is Brewster’s angle?
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
How would you find the thickness of a quarter-waveplate?
t(1/4) = (1/4) x (λ) / (ne - n0)
How would you find the thickness of a half-waveplate?
t(1/2) = (1/2) x (λ) / (ne - n0)
How does subtractive colour work?
Subtractive primaries relfect two of the RGB.
This means that only one of the RGB is absorbed.
How does additive colour work?
Additive primaries relfect one of the RGB.
This means that two of the RGB are absorbed.
Additive Colour System
Red + Green = ?
Additive Colour System
Red + Green = Yellow
Additive Colour System
Red + Blue = ?
Additive Colour System
Red + Blue = Magenta
Additive Colour System
Blue + Green = ?
Additive Colour System
Blue + Green = Cyan
Give the equation for angular magnification for a telescope.
M = -fo / fe
Where:
fo is the focal length of the objective lens
fe is the focal length of the eyepiece
What is the wavelength of red light?
λ(red) ~ 650nm
What is the wavelength of green light?
λ(green) ~510nm
What is the wavelength of blue light?
λ(blue) ~450nm
How do you find the critical angle?
sin(θc) = ne / n0
How would you find the coherence time for a given frequency bandwidth?
t(c) = 1/f
How do you find the coherence length of a laser beam?
L = c t(c)
Where:
L is the coherence length
c is the speed of light
t(c) is the coherence time
How would you find the position (distance from central fringe) of a maximum for Young’s Double Slit experiment?
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
Describe briefly what is meant by Fresnel diffraction.
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.
Describe what is meant by temporal coherent light.
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
How would you find the angle of a first order diffraction with an angle of incidence?
nλ = d(sinθ - sinθi)
What does NA stand for?
Numerical Aperature
What is the formula for NA?
NA = n sinθ
What is the equation for microscopic resolution?
Δx = λ / 2(NA)
What should you assume the wavelength of light is?
550nm
How do you calculate birefringence?
ne - n0
Why do most optical fibre telecoms systems operate in the infra-red part of the EM spectrum?
- 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
Describe a common practical application for the phenomenon of polarisation by reflection.
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.
Describe how the diameter (aperture) of a telescope is a critical parameter when considering the capabilities of the instrument.
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
What is Malus’ Law?
I(θ) = I(0) cos^2θ
Where:
I(0) is the initial intensity
I(θ) is the intensity due to the angle
What is normal dispersion?
It is generally obsereved that the refractive index decreases with increasing wavelength.
This is called normal dispersion.
What is anomalous dispersion?
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.
What is the Rayleigh criterion for a circular aperture?
sinθ = 1.22λ / D
Where:
θ is the angular resolution (radians)
λ is the wavelength of light
D is the diameter of aperture
What is the Rayleigh criterion for a single slit?
sinθ = λ / D
Where:
θ is the angular resolution (radians)
λ is the wavelength of light
D is the diameter of aperture
