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The Wave Nature of Light - Coggle Diagram
Interference and Diffraction:
- any kind of wave can exhibit interference and diffraction because they're just manifestations of the principle of superposition
- this states that the net wave disturbance at any point, due to +2 waves, is the SUM OF THE DISTURBANCES
- Waves from independent sources are incoherent
- They don't maintain fixed phase relationship with each other
- Cannot accurately predict the phase (i.e. whether the wave is at a max or zero) at one point given the phase at another point
- incoherent waves have rapidly changing phase relationships
- results in an averaging out of interference effects so that the total intensity is the SUM OF THE INTENSITIES of individual waves
- only superposition of coherent waves produces interference - these waves must be locked in with fixed phase relationship
- coherent and incoherent waves are idealised extremes
- if 2 waves are in step with each other (i.e. the crest of one falling at the same point as the other), they're said to be in phase
- phase difference between 2 waves in phase is a integral multiple of 2 pi radians
- The Superposition of 2 waves in phase has an amplitude = SUM OF 2 WAVES AMPLITUDES
EXAMPLE: 2 SINUSOIDAL WAVES in phase have an electric field amplitudes of 2E0 and 5E0.
- when the two amplitudes are added together the sum of A is 2E0 + 5E0 = 7E0
- Superposition of 2 waves in phase are called constructive interference
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- two waves that're 180 degrees out of phase are a half cycle apart.
- i.e. the crest of one wave the other is at the trough of another wave
- these sort of waves are called destructive interference
- phase difference is an odd multiple of pi radians
EXAMPLE:
- 2 waves with Amplitudes 2E0 and 5E0 gives a total amplitude : 5E0 - 2E0 = 3E0
- if the 2 waves have the same amplitude there would be a complete cancellation
- the Superposition would have an amplitude and intensity = 0
- for unequal amplitudes to determine the intensity is as follows.
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- in interference, 2+ coherent waves travel different paths to a point where we observe the superposition of the two
- paths may vary in length, pass through different media, or both
- difference in path lengths introduces phase difference (i.e. changes phase relationship between waves)
EXAMPLE: suppose 2 waves start in phase but travel different paths in same medium to a point where they interfere
- difference in path lengths is an integral number of wavelengths
- one wave is simply going through a whole number of extra cycles, which leaves them in phase (i.e. interfere constructively)
- path lengths that're integral multiples of wavelength can be ignored as they don't change the relative phase between 2 waves
Thin Films
- rainbow-like colours in bubbles and oil are produced by interference
- at each surface of film, some light is reflected and some transmitted
- whether the light is reflected or transmitted through it, we can see the superposition of rays that have travelled different paths
- the interference between these rays produces colours
YOUNG'S DOUBLE-SLIT INTERFERENCE EXPERIMENT:
- Coherent light of wavelength illuminates a mask in which 2 parallel slits were cut
- each slit has width A and is comparable to wavelength and length L >> A
- the centres of the slits are separated by distance D
- when light from slits is observed on a screen at a great D from slits
- the centre to centre distance between slits is D
- from the midway point between the slits is a line perpendicular to the mask extends toward the centre of interference pattern on the screen and a line making and angle theta to the normal can be used to locate a particular point to either side of the centre of interference pattern
- cylindrical wave fronts emerge from slits and interfere and form a pattern of fringes
- light from a single narrow slit spreads out primarily in direction perpendicular to the slit, since the wave fronts coming it are cylindrical
- hence the light from one narrow slit forms a band of light on the screen
- light doesn't spread out significantly in the direction parallel to the slit since the slit length (L) is large relative to wavelength
- with two narrow slits the two bands of light on the screen interfere with each other
- the light from the slits starts out in phase, but travel different paths to reach screen
- it is expected that constrictive interference at the centre of interference pattern since waves travel same distance (i.e. are in phase when they reach screen)
- theta = 0
- constructive interference also occurs wherever path difference is an integral multiple of wavelength
- destructive interference occurs wherever path difference is an odd number of 1/2 wavelengths
- gradual transition between constructive and destructive interference occurs since path difference increases continuously as theta increases
- this leads to characteristic alternation of bright and dark bands
- maximum interference at screens is produced by constructive interference
- the path difference is an integral multiple of the wavelength
- antinodes are locations of maximum amplitude
- nodes are locations of minimum amplitude
whether in EM or mechanical waves
Gratings - instead of having 2 parallel slits, a grating, consists of a large number of parallel, narrow, evenly spaced slits
- slit separation of grating is characterised by slit density (i.e. the number of slits per cm)
- slit density is reciprocal of slit separation D
- gratings are made with slit densities of about 50,000 slits/cm
- the smaller the slit separation, the more widely different wavelengths of light are separated by the grating
- transmission gratings light is viewed that is transmitted by the transparent slits of the gratings
- reflection grating instead of slits, has a large number of parallel, thin reflecting surfaces separated by absorbing surfaces
- Huygen's principle, the analysis of reflection grating is the same as for the transmission grating, except that direction of travel for wavelets is reversed
- if an obstacle to light is large relative to the wavelength then geometric optics gives a good approximation to what actually happens
- if the obstacle is not large compared with wavelength we use Huygens's principle to show how waves diffracts
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- image of a wave front reaching a barrier with an opening in it
- every point on the wave front acts as a source of spherical wavelets
-points on the wave front that're behind the barrier have their wavelets absorbed or reflected
- propagation of the wave is determined by wavelets generated by unobstructed parts of wave front
- Huygens constructions suggest the wave diffracts around edges of the barrier
- shows the diffraction pattern formed by light passing through a single slit
- wide central maximum contains most of light energy
- central maximum is usual way to refer to entire bright band in centre of pattern
- actual maximum is at theta = 0
- intensity is brightest right at centre and falls off gradually until first minimum on either side where screen is dark (i.e. intensity is 0)
- continuing away from centre, maxima and minima alternate with intensity changing gradually between them
- according to Huygens's principle the diffraction of light is explained by considering every point along the slit as sources of wavelets.
- light intensity at any point beyond slit is superposition of these wavelets
- wavelets start out in phase but travel different distances to reach a given point
- structure in diffraction pattern is a result of interference of wavelets
-grating allows us to find out where the minima are without need of complicated maths
- two rays that represent propagation of 2 wavelets
- one from the top edge and one from exactly halfway down
- rays are going off at the same angle theta
- lower one travels extra distance 1/2 A
- if extra distance equal to 1/2wavelength then these 2 wavelets interfere destructively
- since every pair interferes destructively no light reaches the screen at the angle
- 1st diffraction minimum occurs where
- calculating angles:
- location of first minimum :
- tells the diameter of central maximum
- contains 84% of the intensity of diffracted light
- size of central maximum is what limits the resolution of optical instrument
RAYLEIGH'S CRITERION
- two sources can just barely be resolved if centre of one diffraction pattern falls at the first minimum of the other
- light from one source travels through vacuum and enters a circular aperture of diameter A
- if is the angular separation of two sources as measured from the aperture and wavelength 0
- is the wavelength of light in vacuum, then sources can be resolved if
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