Waves and optics Flashcards
What is a wave?
A disturbance in a medium which transfers energy without transferring mass.
What is the amplitude, wavelength, and frequency of a wave?
Amplitude - The maximum displacement of a particle from its equilibrium position.
Wavelength - The minimum distance between two points on the wave that are in phase.
Frequency - No. of complete waves the pass a point per second
What is the phase difference for two points on a wave that are:
- in phase?
- in antiphase?
- out of phase?
Points seperated by an integer multiple of wavelengths (λ, 2λ, 3λ, etc) will be in phase.
Δø = 0, 2π, 4π, 6π, etc.
Points seperated by an odd integer number of half wavelengths (λ/2, 3λ/2, 5λ/2, etc) will be in antiphase.
Δø = π, 3π, 5π, etc.
Any other Δø is described as being “out of phase”.
What is the equation for the phase difference between two points on a progressive wave?
phase difference (rad.) = 2pi x separation between points/wavelength
Δø = 2π x Δd/λ
What are the wave equations? (3)
f = 1/T
v = fλ
c = fλ
How do you calculate phase differences on a stationary wave?
Δø = no. of nodes between points x π
Describe the nature of a longitudinal wave and give 2 examples
Direction of the oscillation of particles is parallel to the direction of energy transfer
- Sound Waves
- Seismic P-Waves
Describe the nature of a transverse wave and give 2 examples
Direction of the oscillation of particles is perpendicular to the direction of energy transfer
- Electromagnetic waves
- Seismic S-Waves
What is the speed of an electromagnetic wave in a vacuum?
3x10^8 ms-1
What does it mean for a wave to be polarised, and what type of waves can be polarised?
To polarise a wave is to limit the direction of the oscillation of particles to only one direction. All particles will then oscillate in the same plane.
Only applies to transverse waves, particularly EM waves.
What are some applications of polarisers?
Sunglasses - Polarising filters reduce the glare
EM Transmission - Arials for radio, satellite signals
Polarimetry - Measuring concentration of certain chemicals
What is the principle of superposition?
When two waves of the same type meet, the overall displacement at any point is the sum of the individual displacements of the waves at that point.
“The waves superpose”
What is a stationary wave and how are they formed?
- Formed when two waves with the same frequency travelling in opposite directions superpose
- At some points, the waves superpose in phase, producing antinodes.
- At other points, the waves always superpose in antiphase, producing nodes.
- The frequency/wavelength of the stationary wave is the same as that of the progressive waves that form it.
- Stationary waves store energy instead of transferring it like progressive waves
What is a node and why is it formed?
Nodes are regions where there is no vibration from the equilibrium position.
They are formed when two waves superpose in antiphase.
What is an antinode and why is it formed?
Antinodes are regions where amplitude is at a maximum.
They are formed when two waves superpose in phase.
How do the wavelengths of the harmonics on a string compare to the length of a string?
λₙ = 2L / n, where L is the length of the string
How can the frequencies of the harmonics on a string be calculated?
fₙ = n x f₁
What are the differences between progressive and stationary waves?
Progressive Waves:
- Every point has the same amplitude
- Δø = 2π x Δd/λ
Stationary Waves:
- Amplitude varies from a maximum at an antinode to a minimum at a node
- Δø = no. of nodes between points x π
What is the first harmonic equation?
f₁ = 1/2L x √(T/μ)
where f₁ is the frequency of the first harmonic (m)
L is the vibrating length of the string (m)
T is the tension in the wire (N)
μ is the mass per unit length, kg.m⁻¹
What factors of the string determine the frequency of its first harmonic?
- Length
- Thickness
- Material
- Tension
What is the range of visible wavelengths and in what order are the colours found?
400 - 700 nanometres
violet is found at the 400 end
red is found at the 700 end
What does it mean for a light source to be monochromatic?
Single wavelength
What does it mean for two light sources to be coherent?
- Same frequency/wavelength
- Constant phase relationship
What is the relationship between path difference and phase difference?
Δø = 2π x Δd/λ
where Δø is the phase difference (rad.)
Δd is the path difference (m)
I REALISED WHAT THIS IS SAYING IT JUST MEANS THAT THEY’RE PROPORTIONAL
so if Δø = 2π, Δd = 1 (i think?) (both of those are in phase)
and if Δø = π, Δd = 1/2
What assumptions are made when deriving the double slit formula?
- The light is monochromatic
- Each slit acts as a source of coherent waves
What is the double slit formula?
W = λD/s
Where W = fringe width(m)
λ is wavelength (m)
D is slit-to-screen seperation (m)
s is seperation
What is the path difference equation?
When the path difference is equal to nλ (n = integer), the rays from every slit will superpose in phase producing a maximum.
sinθ = Δd/d
where:
Δd = path difference
d = grating spacing
T
What is diffraction?
The spreading out of waves after passing through an opening or around an obstacle.
What is the pattern observed when monochromatic light is shone through a single slit?
- Each slit acts as a source of coherent waves. These waves diffract after passing through each slit and superpose with one another.
- Bright patches (maxima) form when waves suerpose in phase, causing constructive interference.
- Dark patches (minima) form when waves superpose in antiphase, causing destructive interference
- As the orders increase, the fringes become progressively dimmer
What is the pattern observed when white light is shone through a single slit?
- Bright central white 0ᵗʰ order beam
- Higher orders are split into spectra, with violet closest to the centre and red furthest from the centre
- As the orders increase, the maxima become wider
- Higher order maxima may overlap and longeer wavelengths may not be seen
How does the width of the central maximum vary with the slit width?
The width of the central maximum is inversely proportional to the slit width.
Narrower slit = wider central maximum, but dimmer pattern
How does single slit diffraction affect the pattern from a double slit experiment?
Due to single slit diffraction, a real double slit experiment will see the fringe intensity decrease from the centre.
(its the graph with the graph within a graph if you get what i mean)
What is the relationship between the grating spacing and the number of lines per metre?
d = 1/(no. of lines per metre)
where d is the grating spacing
What is the equation for the highest order maximum seen?
nₘₐₓ = d/λ, rounded down
where nₘₐₓ is the max order
d is the grating spacing
λ is the wavelength
What are some uses of diffraction gratings?
- Determining the wavelength of an unknown source of light
- Spectrometry - astrophysics - identifying the composition of stars
- Spectrometry - chemistry - identifying chemical composition of a sample
- Select a specific wavelength from a spectrum
- Entertainment (lightshows, etc)
What is the diffraction grating formula?
sin(θₙ) = nλ/d
n.λ = d.sin(θₙ)
where:
θₙ = angle between 0ᵗʰ and nᵗʰ orders
d = grating spacing (m)
λ = wavelength (m)
n = order
What is refraction?
The bending of light when it crosses the boundary between two transparent median of different refractive indices, at an angle to the normal
What is the refractive index of a material and how is it calculated?
A measure of how much the speed of light is reduced within a given medium compared to its speed in a vacuum. Only the wavelength changes, not the frequency
Refractive index = wavelength in a vaccum / wavelength in the medium
Name some of the refractive indices you should expect for air, water, glass and diamond (TAZARLORD REFERENCE?)
- Air - 1
- Water - 1.33
- Glass - 1.5
- Diamond - 2.4
Which angle is used in Snell’s Law calculations?
The angle between the light ray and the normal
What is total internal reflection (TIR)?
Occurs when:
- The angle of incidence is greater than the critical angle (θ₁ > θ꜀)
- Light travels from a denser medium to a less dense medium (refractive indices) (n₁ > n₂)
What is the critical angle?
(AI Generated answer FUCK THIS TOPIC)
Definition of Critical Angle:
The critical angle is the angle of incidence in the denser medium at which the angle of refraction in the less dense medium is 90 degrees. At this angle, the refracted ray travels along the boundary between the two media.
If the angle of incidence is greater than the critical angle, total internal reflection occurs, and no light is refracted into the less dense medium.
If the angle of incidence is less than the critical angle, the light is partially refracted and partially reflected.
What are the two components of a fibre optic cable and their functions?
Core - Where the light travels through. Has a higher refractive index than the cladding.
Cladding - Promotes TIR at core-cladding boundary, protects the core from scratches, prevents ‘cross talk’ (where signals cross from one core to a neighboring core in the bundle)
What is material dispersion, why does it occur and how can it be mitigated?
Transparent materials have different refractive indices for different frequencies of light. Generally, shorter wavelengths = higher refractive index.
Different refractive indices mean that idfferent colours travel at different speeds down an optical fibre.
Limiting material dispersion - use monochromatic signals
What is modal dispersion, why does it occur and how can its effects be mitigated?
Light rays taking different paths (“modes”) down the cable of different lengths, and therefore taking different times.
Limiting modal dispersion - use narrower cores, make the n(cladding) close to n(core) so that θ꜀ is big, limiting the potential of different modes
What happens when n₁ > n₂, and when n₂ > n₁?
n₂ > n₁ = ray reflects towards the normal
n₁ > n₂:
- θ₁ < θ꜀ = ray reflects away from the normal
- θ₁ = θ꜀ = ray refracts along the boundary
- θ₁ > θ꜀ = ray undergoes TIR
