Optics - kerboodle Flashcards
5.1 Refraction of light
- The wave theory of light is used to explain the reflection and refraction of light
- diagrams are used more often when considering the effects of lenses or mirrors on the path of light
- The diagrams we use normals as well as the predicted direction of the light, with the predicted direction of the light being called light rays
- Light rays represent the direction of travel of the wavefronts
- The normal is an imaginary line perpendicular to a boundary between two materials or a surface
- Refraction is the change of direction that occurs when light passes at an angle across a boundary between two transparent substances
- When a light ray enters a glass block, it will bend towards the normal, however when it leaves it will bend away from the normal.
- No refraction occurs if the incident light ray enters through the normal
- At a boundary between two transparent substances, the light ray bends towards the normal if it passes into a more dense substance and away from the normal if it passes into a less dense substance
5.2 More about refraction
Explaining refraction
- Refraction occurs because the speed of the light waves is different in each substance
- The amount of refraction that takes place depends on the speed of the waves in each substance
- The frequency of waves does not change when refraction occurs
Refraction at a boundary between two transparent substances
• If the light passes from a less dense object into a more dense object, the light will bend towards the normal
• If the light passes from a dense object into a more dense object, the light will bend away from the normal
• the equation for figuring out the refractive index, as well as the angles of the light as it passes/leaves an object is:
n1 * sinθ1 = n2 * sinθ2
• This equation is given by Snell’s law
• The refractive index can also be calculated using the speed of light in a vacuum divided by the speed of light in a transparent substance
The white light spectrum
- White light is a combination of all the spectrums of visible light
- You can split white light into the different colours of the spectrum by using a prism
- This happens because the different colours have different wavelengths, and as shorter wavelength = greater the amount of refraction, they will be ordered by their wavelengths
5.3 Total internal reflection
Investigating total internal reflection
- When a light ray travels from a glass into the air, it refracts away from the normal
- If the angle of incidence is increased to a certain value known as the critical angle, the light ray refracts along the boundary
- If the angle of incidence is increased past the critical angle, the light ray undergoes total internal reflection
- Total internal reflection can only occur if the incident substance has a larger refractive index than the other substance, as well as the angle of incidence exceeding the critical angle
- The critical angle is calculated by taking the sin of the refractive index of one of the substances and dividing it by the refractive of the other
Why do diamonds sparkle when light is directed at them
- When light enters a diamond, it is split into the colours of the spectrum
- As diamond has a very high refractive index (2.417) it separates the colours more than any other substance does
- This high refractive index also gives the diamond a critical angle of 24.4°
- This factor of having allow critical angle means that light can undergo many total internal reflections before the light leaves diamond
- This means that its colour is spread out more and more, and sparkles with different colours as the light leaves the substance.
Optical fibres
- Optical fibres are used in medical endoscopes to see inside the body, and in communications to carry light signals
- In optical fibres, the light goes through total internal reflection every time it reaches the boundary
- A communications optical fibre allows pulses of light that enter from one end, from a transmitter, to reach a receiver at the other end.
- Optical fibres used in communication need to be highly transparent to minimise absorption of light, which would otherwise reduce the amplitude of the pulses progressively the further it travels in the fibre
- Total internal reflection takes place at the core-cladding boundary through which the light travels, without cladding the light would crossover to other wires meaning the signal would not be secure
- In optical wires the core must be very narrow to prevent modal dispersion, this occurs in a wide core because the light travelling along the axis of the core travels a shorter distance per metre of fibre than light that repeatedly undergoes total internal reflection, if this occurs, a pulse of light might merge with the next pulse, causing errors in the signal.
5.4 Double Slit Interface
Young’s double-slit experiment
• Proved evidence that light was a wave, not a particle as Isaac Newton believed
• Works by having a light source aimed at two slits, these slits act as coherent sources of waves, meaning they emit light waves with a constant phase difference and the same frequency
• This means that there are points where the waves caused by the two coherent sources superpose, and since the phase difference would be different depending on what area they superimpose at, it would lead to either a minima or maxima
• At points of minima dark fringes are visible, while at points of maxima, bright fringes are visible
• In Young’s slit experiment the fringes are evenly spaced and parallel to the double slits
• IF the sing slit used to focus the light is too wide, it can lead to the dark fringes of the double-slit pattern becoming narrower than the bright fringes, and contrast between the dark fringes and the bright fringes is lost.
• A laser beam from a low power laser can be used instead of a lamp and a single slit, but it must be shone at a card as it could damage the retina if the light enters the eye
• The fringes seen in the double-slit experiment are formed from the interference of light from the two slits:
• Where a bright fringe is formed, the light from one slit reinforces the light from the other slit.
• When a dark fringe is formed, the light from one slit cancels the light from the other slit, meaning that they arrive at 180° out of phase
• The equation for fringe separation is
w = (λ * D)/s, where λ is the wavelength of light, D is the distance from the slits to the screen and s is the slit spacing, which is the distance between the centres of the slits.
• The equation shows that the fringes become more widely spaced if: the distance D from the slits to the screen is increased, The wavelength λ of the light is increased and the slit spacing, s, is reduced.
The theory of the double slit equation
- The theory behind the double-slit experiment is that the two coherent waves are released with the same properties (wave speed, wavelength, amplitude, etc.)
- Because of this, unless its the middle point, one wave will always arrive before the other
- As one wave arrives before the other, one wave will always arrive at a different point in phase.
5.5 More about interference
Coherence
• Double slits are described as coherent sources because they emit light waves of the same frequency with a constant phase difference (provided it is lit with a focused light source)
Wavelength and colour
- In the double-slit experiment, the fringe separation depends on the colour of light used.
- As the fringe spacing equation shows that wavelength is a factor, using different colours as the light will result in different fringe patterns
Light sources
- Vapour lamps and discharge tubes produce light with a dominant colour, meaning they will produce light of one colour
- Other colours may be emitted, but the primary colour will be much more intense
- this means that in effect, they can be monochromatic light sources since they emit light with a spectrum which is dominated by one wavelength
- Light from a filament lamp or the sun is composed of the colours of the spectrum and therefore covers a continuous range of wavelengths from about 350nm to 650nm
- These two cases can differ when laser light is used
- Laser light is highly monochromatic, meaning the wavelength can be specified within a nanometre
- A laser is also a convenient source of coherent light, since the light does not need to pass through a single slit first it is much more useful than light sources such as lamps or discharge tubes.
- It is also a useful coherent source of light since the photons which make up the light cause more photons to be emitted, they are all in phase, rather than the other light sources which emit photons randomly
White light fringes
- For white light fringes, instead of having minimas or maximas, you instead have the different colours of light, this is due to the fact as they all operate on different wavelengths, a minima for one colour might be a maxima for another, leading to the spot having the colour of a different light rather than of a dark fringe
- When white light is used, the central fringe will always be white, this is because every colour contributes to central fringe
- the inner fringes are tinged with blue on the inner side and red on the outer side, this is because red fringes are more spaced out than blue because of their differing wavelengths
- The outer fringes merge into an indistinct white light becoming fainter with increasing distance from the centre, this is because, where the fringes merge, different colours reinforce and therefore overlap.
5.6 Diffraction
Observing diffraction
• Diffraction is the spreading of waves when they pass through a gap or by an edge
• It is a general property of all waves and it important for the design of optical instruments
• Diffraction is usually different depending on the wave, for a light wave to diffract, a much smaller gap is needed than for a sound wave, this is because a sound wave’s wavelength is much larger than that of light
• Diffracted waves spread out more if the gap which they diffract through is made narrower or the wavelength is made longer
• Diffracted waves have broken on either side of the centre, due to the waves superimposing and cancelling out at those sections.
• Diffraction of light by a single slit can be demonstrated by directing a parallel beam of light at the slit
• the pattern formed shows a central fringe with further fringes on either side of the central fringe, the intensity of each fringe decreases as it gets further from the central fringe
Notes
• The central fringe is twice as wide as each of the outer fringes
• the peak intensity of each fringe decreases with distance from the centre
• Each of the outer fringes has the same width
• The outer fringes are much less intense than the central fringe
More about single slit diffraction
• If the single slit pattern is observed:
Using different sources of monochromatic light in turn, the observations show that the greater the wavelength the wider the fringes
Using an adjustable slit, the observations show that making the slit narrower makes the fringes wider.
• It can be shown theoretically that the width of the central fringe can be given by the wavelength of the light divided by the width of the single and then multiplied by 2 times the distance (w = (λ/a) * 2D)
• Therefore the width of each fringe is proportional to λ/a.
• This can show how different colours of light can also affect the fringe pattern if blue light is used the fringes would be narrower than if the red light was used since the wavelength is smaller
