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Waves and the Particle Nature of Light (Wave Basics (Describing Waves…
Waves and the Particle Nature of Light
Wave Basics
Progressive wave carries energy from one place to another without transferring material ∴ source of wave loses energy - transfer of energy in same direction as wave is travelling
Describing Waves
Displacement, x - how far a point on the wave has moved from its undisturbed position
Amplitude, A - maximum magnitude of displacement
Wavelength, λ - length of one whole wave cycle
Period, T - time taken for a whole wave cycle to complete
Frequency, f - number of cycles per second passing a given point
Phase - measurement of the position of a certain point along the wave cycle (angle)
Two points in phase if at same point on wave cycle - must have same displacement + velocity + phase difference 2π - exactly out of phase if phase difference π
Wavefronts will occur if two or more coherent, in phase waves travel in the same direction - imaginary planes that cut across all waves joining the points that are in phase - distance between each wavefront = λ
Phase difference - amount one wave lags behind another
Oscilloscopes
Measures voltage - displays wave from signal generator as function of voltage over time - displayed wave = trace
Screen split into squares (divisions)
y axis = volts per division - controlled by gain dial
x axis = seconds per division - controlled by timebase dial
period = "number of divisions in one complete cycle" x "timebase setting"
EM Waves
Transverse - vibrations at right angles to direction of travel
Travel at speed of light in a vacuum
Consist of vibration electric and magnetic fields at right angles to each other and the direction of travel
Can be reflected, refracted, diffracted, polarised, undergo interference and obey v=fλ
Reflection - wave bounces back when it hits a boundary
Refraction - waves changes direction when it enters a different medium due to change in speed
Carry energy
Intensity = rate of flow of energy per unit area at right angles to direction of travel of the wave
Longitudinal - vibrations parallel to direction of travel
e.g. Sound Waves - consist of alternate compressions (higher pressure) and rarefactions (lower pressure) so cannot travel through a vacuum - λ = compression to compression
Superposition
Principle of superposition - when two or more waves cross, resultant displacement = vector sum of individual displacements
Interference - when two or more waves superpose with each other
Crest + crest/trough + trough = constructive interference
Path difference = nλ
Crest + trough = destructive interference - must have similar amplitude to be noticeable - total when equal size
Path difference = (n+0.5)λ
Must have coherent sources for clear interference patterns - same wavelength, frequency and fixed phase difference
Observe with sound waves
Connect two speakers to same oscillator so waves in phase and coherent
When walking across room in front of speakers, varying volumes will be heard
Stationary wave = superposition of two progressive waves with same wavelength, moving in opposite directions
No energy transmitted by stationary wave
To demonstrate:
Attach vibration transducer at one end of stretched string and fix other end
Transducer given wave frequency by signal generator and creates wave by vibrating string
Wave reflected back and forth
At most frequencies, interference pattern is a jumble but if signal generator altered so transducer produces exact number of waves in time taken for a wave to get to the end and back again, original and reflected waves reinforce each other - occurs at resonant frequencies - pattern doesn't move
Each particle vibrates perpendicular to the string
Node where amplitude of vibration is zero
Antinode - point of maximum displacement
At multiples of resonant frequency, exact number of half wavelengths fit onto string
Demonstrate with sound waves - lay powder along bottom of glass tube - powder shaken away from antinodes and undisturbed at nodes
Phenomena
Refraction
Bends towards normal - slowing down - speed changes as wavelength changes and frequency remains constant
Refractive index - ratio between speed of light in a vacuum and speed of light in that material
Critical angle - angle of incidence when angle of refraction 90° - total internal reflection occurs and angles of incidence greater than C
Lenses change direction of light rays by refraction
Converging lenses bring light rays parallel to the principle axis onto the principle focus on focal plane - focal length = distance between lens axis and focal plane
Real image when light rays from point on an object made to pass through another point in space - light rays can be captured on a screen
Diverging rays trace back with virtual rays to a point at which the rays appear to have come from - focal length = distance between lens axis and principal focus (-ve)
Virtual image formed by converging or diverging - when light rays from point on an object appear to have come from another point in space - image cant be captured on a screen
Power of a lens - its ability to bend light - higher power, more refrection
If two or more thin lenses in line with principal axes lined up - total power = sum of individual powers
Polarisation
Plane polarisation - polarising a wave so that it only oscillates in one direction
For polarised light - plane of polarisation always perpendicular to the direction of the propagation of light
When transmission axes of two polarising filters parallel, all light that passes through the first filter passes though the second
when perpendicular, no light passes through second filter
At certain angles, light is partially polarised when it is reflected - intensity of reflected ray can be reduced by viewing it through a polarising filter
remove unwanted reflections in photography
remove glare with polaroid sunglasses
Diffraction
Way that waves spread out as they come through a narrow gap or go around an object
When wave meets an obstacle, diffraction occurs around the edges to form a shadow behind where the wave is blocked - wider obstacle compared to wavelength = less diffraction = longer shadow
Most diffraction when gap same size as wavelength - any smaller, waves will be reflected
If wavelength of light roughly similar to aperture, diffraction pattern of light and dark fringes for coherent source or series of spectrum for white light
Longer wavelength compared with slit = wider diffraction pattern
Huygen's Construction
Every point on a wavefront may be considered to be a point source of secondary wavelets that spread out in the forward direction at the speed of the wave. The new wavefront is the surface that is tangential to all of these secondary wavelets
Diffraction Gratings
If monochromatic light passed through a grating, interference pattern really sharp as so many beams reinforce the pattern
When monochromatic light passed through slits, light is diffracted at both slits producing two coherent light sources and an interference pattern
d = slit spacing
θ = angle between order and zero order
n = order
Reflection
Ultrasound
Boundary between two media = interface
When a wave travels from one medium to another, some energy is reflected, some transmitted - proportion depends on difference in densities - similar = more transmitted
Sound waves that have too high a frequency for humans to hear
To resolve object λ ≥ diameter
Short pulses and log gap produce clearer images as reflected waves reach transducer after pulse finished but before next pulse sent
Shorter wavelength also increases quality as less diffraction
Wave-Particle Duality + Photoelectric Effect
"If 'wave-like' light shows particle properties, 'particles' like electrons should be expected to show wave-like properties"
de Broglie wavelength - can be interpreted as probability wave - likelihood of finding a particle at a point directly proportional to the square of the amplitude of the wave at that point
Electrons first diffracted in 1927 - diffraction patterns observed when accelerated electrons in vacuum tube interact with spaces between carbon atoms in polycrystalline structure
Smaller accelerating voltage = slower electrons = shorter λ = smaller spread of lines
Electron microscopes favoured over light as shorter wavelength so less diffraction effects to blur details
When light from hot gas split with prism:
Heating gas excites atoms
As electrons fall back, energy emitted as photons
Splitting light gives line emission spectrum
When white light passed through cool gas then prism:
Most electrons in their ground state
Photons of correct wavelength absorbed by electrons to excite them
Gives line absorption spectrum
Interference + diffraction patterns of light can only be explained by wave theory
Wave Theory:
For particular frequency of light, energy carried is proportional to intensity
energy carried spread evenly over wavefront
each electron on surface would gain small amount of energy from each incoming wave so gradually each electron would gain enough energy to leave metal
EM waves can only be released in discrete packets - quanta - photons - acts as particle and will either transfer all or none of its energy when interacting with another particle
Electrons can only exist in well-defined energy levels - can move down energy levels by emitting a photon, or move up (excitation) by absorbing one - energy carried by photon equal to difference in energies between two levels - emitted photons can only take certain value of frequency
Electronvolt eV used as unit of energy - KE carried by an electron after it has been accelerated through a potential difference of one volt
Photoelectric effect - shining high frequency (UV) light onto surface of metal causes metal to emit electrons - free electrons on surface absorb energy from light , if enough energy absorbed, bonds holding electron to metal break and electron released as photoelectrons
Conclusions:
For a given metal, no photoelectrons are emitted if radiation has frequency below the threshold frequency
KE of emitted photoelectrons range from zero to a maximum - value of maximum KE increases with frequency of radiation but unaffected by intensity of radiation
Number of photoelectrons emitted per second proportional to intensity of radiation
KE independent of intensity as electrons can only absorb one photon at a time and increasing intensity does not increase energy of individual photons
