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Covers basic knowledge, definitions and questions for refraction, diffraction and interference phenomena of waves. https://www.savemyexams.com/a-level/physics/aqa/17/revision-notes/3-waves/3-5-refraction/3-5-3-fibre-optics/
What does it mean when waves are coherent?
Two waves have the same frequency, wavelength and have a constant phase relationship (i.e. fixed phase difference)
How are dark and bright fringes formed in Young’s double-slit experiment?
A coherent light source is shone through the slits
When the light shines through the slits, a path difference is created
Where the path difference is nλ (n being an integer), constructive interference is caused to form a bright fringe.
Where the path difference is nλ (where n is fractional) destructive interference is caused to form a dark fringe.
What is a condition for the double-slit experiment or to use the equation: w = (λD)/s and dsinθ = nλ
These equations rely on very small angles in order to assume that the two paths of light are parallel.
The small angle approximation only occurs when the distance from slit to screen is much larger than the distance between the two slits
(approx 2000x larger)
How does Young’s single-slit experiment work?
When a wave passes through an aperture (slit) with a width smaller than the wavelength of the source (d<λ)
This causes a diffraction pattern to appear
Central maximum appears with lower intensity maxima either side.
Central maximum is twice as wide as other maxima
What does the diffraction pattern look like when white light is used?
central bright fringe is white
fringes in the next orders alternate colours from violet being closest to the central maximum, and red being the furthest
This occurs because red light has a larger wavelength and λ is directly proportional to w. Therefore when λ increases, w increases, leading to red being the outermost colour on the diffraction pattern.
Light of different wavelengths are diffracted by different amounts
List the safety precautions for Young’s double slit experiment.
Wear laser safety goggles
Don’t shine the laser at reflective surfaces (make sure to look around so beams are not being reflected into people’s eyes)
Display a warning sign
Never shine the laser at a person
What did Young’s double slit experiment imply?
Light was a wave, because only waves had diffraction and interference properties; particles did not. Therefore EM radiation as a whole was a wave.
What is diffraction?
The spreading out of waves when they pass through or travel around a gap
When does the greatest diffraction occur?
When the gap (slit) is the same size as the wavelength. When the gap is smaller than the wavelength most waves are reflected, and if it is larger, the diffraction is less noticeable.
What is the diffraction pattern like with a diffraction grating?
Much brighter and sharper than in Young’s double slit because there are more slits spaced equally apart from each other.
How does the intensity of the interference pattern change with the number of slits?
As the number of slits increases, the intensity of the interference pattern also increases.
What is the zero order?
The centre of the diffraction grating, also known as the central maximum
What is the first order?
The bright fringes either side of the zero order line
What is the formula associated with diffraction gratings?
dsinθ = nλ
Where d is the distance between the slits, θ is the angle to the normal made by the maximum, n is the order, and λ is the wavelength
Derive dsinθ = nλ
Considering the first order maximum, where the path difference between two adjacent rays of light is one wavelength (as shown in the diagram below), name the angle between the normal to the grating and the ray of light θ.
As you can see a right angle triangle is formed, with side lengths d and λ. And by using the fact that a right angle is 90°, and angles in a triangle add up to 180°, you can see the upper angle in the triangle is θ (because the lower angle is 90-θ°).
By using trigonometry we can see that for the first maximum sin θ = , (as sin θ = d λ Opp/Hyp) which rearranges to , (for the first order). dsin θ = λ
We know that the other maxima occur when the path difference between the two rays of light is nλ, where n is an integer, therefore we can generalise the equation by replacing λ with nλ to get: d sinθ λ = n .
What are some examples of diffraction in use?
Light from stars can be split up using a diffraction grating to get line absorption spectra which can be used to show which elements are present in the star.
X-ray crystallography, which is where x-rays are directed at a thin crystal sheet which acts as a diffraction grating to form a diffraction pattern, this is because the wavelength of x-rays is similar in size to the gaps between the atoms. This diffraction pattern can be used to measure the atomic spacing in certain materials.
Is a material with a high refractive index more or less optically dense than a material with a low refractive index?
More optically dense
because n = c/cs where c is the speed of light, and cs is the speed of light in the medium.
How does refraction occur?
When a wave enters from one medium to another, changing the speed of the wave.
What is the principle of reflection?
The angle of incidence is equal to the angle of reflection
When does light refract towards the normal?
From a less dense medium to a more dense medium. i.e. from high to low refractive index.
When does light refract away from the normal?
From a more dense medium to a less dense medium. i.e. from low to high refractive index
Draw Snell’s law
What is the critical angle (θc)?
The angle of incidence at which the angle of refraction is exactly 90°. At this angle, light is refracted along the boundary of the medium.
When does total internal reflection occur?
When the angle of incidence is greater than the critical angle.
The incident refractive index (n1 ) is greater than the refractive index of the material at the boundary (n2 ) i.e. when the light is travelling from a more to less optically dense medium.
What is an example of a use of total internal reflection?
Optical fibres
What is signal degradation?
When the intensity of the signal decreases and information is lost.
What is signal degradation caused by?
Light escaping the glass
Absorbtion: where part of the wave’s energy is absorbed by the fibre, reducing the amplitude of the signal, which could lead to a loss of information
Dispersion: this causes pulse broadening, which is where the received signal is broader than the original transmitted signal. Broadened signals can interfere causing loss of information
When does modal dispersion occur? You can draw a diagram to visualise.
When the light pulses in the optical fibre spread out due to the different angles of incidence in the original pulse. It also causes pulse broadening as the pulses emerging are longer than they should be.
What is material dispersion?
When white light is used to transmit signals instead of monochromatic. The light separates into all of the colours within the visible spectrum, therefore the signal is dispersed and the beam gets wider as it travels down the optical fibre.
It causes pulse broadening.
Where is modal dispersion more prominent?
Some rays of light travel directly through the centre and others are totally internally reflected. With wider cores, there is a larger variance in pathways for light to travel therefore modal dispersion is more prominent.
How can you combat modal dispersion?
Use a very narrow core
How does material dispersion happen?
Light of different wavelengths travel at different speeds through a medium. Therefore they spread out and cause interference. This can result in pulse broadening.
Violet light has the shortest wavelength, so it travels the slowest in the fibre
This means its angle of incidence on the fibre boundary is smallest compared to the other colours
The angle of incidence is equal to the angle of reflection, so the angle of reflection is also smaller
This means it takes longer for the violet colour to travel down the fibre because it undergoes more reflections
How can you combat material dispersion?
Use monochromatic light
What is pulse broadening?
A result of modal and material dispersion where the pulses emerging from the fibre are longer than those entering it
Why is cladding used?
Protect the thin core from damage and scratching
Prevent signal degradation through light escaping the core, which can cause information from the signal to be lost
It keeps the signals secure and maintains the original signal quality
It keeps the core separate from other fibres preventing information crossover
What is a step-index optical fibre?
When the refractive index of the core is more than the refractive index of the cladding, this allows TIR to occur.
The refractive index of each component increases moving from the outside to the centre of the fibre
How does cladding prevent pulse broadening?
When the cladding has a refractive index only slightly beow that of the core, the critical angle for total internal reflection is close to 90°. Consequently, only rays travelling nearly parallel to the axis are totally internally reflected.
How to reduce absorption of a signal in optical fibres?
Use an extremely transparent core (low refractive index)
Use optical fibre repeaters so the pulse is regenerated before significant absorption has taken place
What is absorption of an optical fibre signal and what happens as a result?
When the fibre absorbs part of the signal’s energy
This reduces the amplitude of the signal, which can lead to a loss in the information transmitted
What is the result of pulse broadening?
The merging/interference of pulses, which distorts the information in the final pulse and decreases the amplitude of the signal
How do you prevent pulse broadening?
Use a narrow core to reduce the differences in the path length of the signal (reduces modal dispersion)
Use of a monochromatic source so the wavespeed of the pulse is constant (reduces material dispersion)
Use optical fibre repeaters so the pulse is regenerated before significant pulse broadening has taken place
Use a single-mode fibre, where only a single wavelength of light passes through the core, to reduce multipath modal dispersion
Prove dsintheta = nlambda equation
See Goodnotes.
Equation to get d?
d = 1/N where d is the spacing between adjacent slits and N is the number of lines per unit (usually per metre).
What does a single-slit diffraction pattern look like with white light?
White central maximum with lower intensity maxima either side
Maxima of different colours with blue closest to the central maxima, and red the furthest. Pattern repeats with lower intensity.
What does single-slit diffraction pattern look like with white light through a green filter?
Central maximum with lower intensity maxima either side. Central maximum is twice as wide as the other maxima. Dark fringes between each maximum.
What affects the width of maxima? (Young’s single-slit)
The wavelength of light used. Increasing the wavelength increases the effect of diffraction, therefore the central maximum becomes wider. Its intensity decreases because photons are more spread out.
The width of the slit used. Increasing the slit width decreases the effect of diffraction so the central maximum decreases in width. Its intensity increases as photons are less spread out (e.g. passing light through very wide slit it would not diffract)
How does a single slit make light coherent?
Light has a fixed path difference. FINISH (SEE REDDIT)
