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Physics Section 2 - Waves and Optics

Joseph McAuliffe Physics A-Level English 5.0Average rating 5.0 out of 5 (1 rating)

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4 ~ Waves
- 4.1 Waves and vibrations
  - Types of waves
    - sound, seismic and waves on strings often referred to as mechanical waves
    - em waves are oscillating electric and magnetic fields that progress through space without the need for a substance
      - em waves include radio, micro-, infrared radiation, light, UV radiation, X-rays and gamma radiation
  - Longitudinal and transverse waves
    - longitudinal
      - direction of vibration parallel to direction of propagation
      - eg sound, primary seismic
    - transverse
      - direction of vibration perpendicular to direction of propagation
      - eg em, secondary seismic
  - Polarisation
    - transverse are plane-polarised is vibrations stay in one plane only
    - unpolarised if vibrations change from one plane to another
    - longitudinal waves can't be polarised
- 4.2 Measuring waves
  - Key Terms flashcards
    - Waves Key Terms
  - period of a wave = 1/f
  - Wave speed
    - higher f, shorter λ
    - wave speed c=fλ
  - Phase difference
    - fraction of cycle between vibrations
    - λ=2π (radians)
    - phase difference = 2πd/π
- 4.3 Wave properties 1
  - ripple tank used to study properties
    - waves observed referred to as wavefronts
  - Reflection
    - angle of incidence = angle of reflection
  - Refraction
    - as wave passes boundary at which wave speed changes, λ also changes
    - if wavefronts approach at angle to boundary, they change direction too
    - refract towards normal when entering substance more dense as they slow down
  - Diffraction
    - occurs when waves spread out after passing through a gap or round an obstacle
    - narrower gap results in more spreading
    - longer λ results in more spreading
  - Dish design
    - bigger dish can receive stronger signal because more radio waves reflected by dish onto ariel
    - but bigger dish reflects radio waves to smaller focus as it diffracts waves less ∴ dish needs to be aligned more carefully than smaller dish otherwise radio waves not focussed onto aeriel
- 4.4 Wave properties 2
  - The principle of superosition
    - combining of waves known as superposition
    - when two waves meet, the total displacement at a point is equal to the sum of the individual displacements at that point
    - crest + crest = supercrest > reinforce each other
    - trough + trough = supertrough > reinforce each other
    - crest + trough = zero displacement > cancel each other out
  - Further examples of superposition
    - stationary waves on a rope
      - formed when two people send waves continuously along a rope from either end
        two sets of waves referred to as progressive waves
        combine at fixed point of no displacement or nodes
    - water waves in a ripple tank
      - interference patterns (two circles of waves)
        cancellation where crest meets dipper
        use coherent sources
  - Tests using microwaves
    - demonstrate reflection, refraction, diffraction, interference and polarisation of microwaves
    - eg interference
- 4.5 Stationary and progressive waves
  - Formation of stationary waves
    - harmonics
      - first harmonic sometimes referred to as fundamental mode of vibration
        single loop that has a node at either end and antinode (max. displacement) in centre
      - distance between adjacent nodes = 1/2λ
    - stationary waves that vibrate freely do not transfer energy to their surroundings
  - Explanation of stationary waves
    - amplitude of vibrating particle in stationary wave pattern varies with position from zero at node to max. amplitude at antinode
    - phase difference between 2 vibrating particles
      - 0 if two particles are between adjacent nodes or separated by even no. of nodes
      - π rads if two particles separated by odd no. of nodes
  - Examples of stationary waves
    - sound in a pipe
    - reflecting microwaves against metal plate
- 4.6 More about stationary waves on strings
  - Stationary waves on vibrating strings
    - first harmonic pattern of vibration seen at lowest possible frequency that gives a pattern
      - λ1=2L
      - f=c/λ1=c/2L
    - second harmonic
      - two loops
      - f2=c/λ2=c/L=2f1
    - Pitch
      - relates to frequency
      - raising tension/shortening length inc. pitch
      - lowering tension/inc. length lowers pitch
      - f=1/2l √(T/μ)
        T is tension
        μis mass per nit length
  - Explanation of the stationary wave patterns on a vibrating string
    - crest reverses its phase when it reflects at the fixed end and travels back along the string as a trough
      - when it reaches the vibrator, it reflects and reverses phase again
        if crest is reinforced by crest from vibrator, amplitude of wave increased
    - time for wave to travel along sting and back = 2L/c
    - time for vibrator to pass through whole no. of cycles = m/f
    - 2L/c=m/f
      - f=mc/2L=mf
      - λ=c/f=2L/m
      - length of string L = mλ/2 = whole no. of half wavelengths
- 4.7 Using an oscilloscope
  - Measuring the speed of ultrasound
    - measure horizontal distance on screen from leading edge of the pulse to start of the spot's sweep and multiply it by what the time base control is set to
  - oscilloscope consists of electron tube and associated control units
    - electron gun at one end of glass tube emits electrons in a beam towards a fluorescent screen at other end of tube
      - light is emitted from the spot on the screen where the beam hits the screen
  - How to use an oscilloscope
    - position of spot of light on screen is affected by pd across either pair of deflecting plates
      - displacement of spot is proportional to applied pd
    - to display a waveform
      - X-plates connected to oscilloscope's time base circuit (left to right)
      - pd to be displayed is connected to the Y-plates (up and down)
5 ~ Optics
- 5.1 Refraction of light
  - at boundary light bends
    - towards normal if passes into more dense substance
    - away from normal if passes into less dense substance
  - Investigating the refraction of light by glassd
    - Snell's law
      - sin(i)/sin(r) = refractive index
    - partial reflection when light ray in air enters glass or other refractive substance
  - Comparing glass to air refraction with air to glass refraction
    - i2=r1 and r2=r1
    - as n=sin(i1)/sin(r1), sin(i2)/sin(r2)=1/n
  - Refraction of a light ray by a triangular prism
- 5.2 More about refraction
  - Explaining refraction
    - occurs because speed of light waves is different in each susbtance
    - n(s)=c/c(s)=λ/λ(s)
  - Refraction at a boundary between two transparent substances
    - sin(i)/sin(r)=c1/c2
    - n(1)sinϑ(1)=n(2)sinϑ(2)
  - The white light spectrum
    - use prism to split a beam of white light into colours of the spectrum
      - white light is made up of different wavelengths
        shorter wavelengths diffract more
- 5.3 Total internal reflection
  - Investigating total internal refection
    - at critical angle, light ray refracted along boundary
    - beyond critical angle, light ray reflected - total internal reflection at boundary
    - TIR can only take place if:
      - incident substance has larger refractive index than the other substance
      - angle of incidence exceeds critical angle
    - sinϑc=n2/n1 when ϑc is the critical angle
  - Who do diamonds sparkle when white light is directed at them?
    - high refractive index so small critical angle meaning colours spread out more and more before it emerges
  - Optical fibres
    - used in endoscopes
    - fibres consist of core surrounded by layer of cladding of lower refractive index to reduce light loss from core which would reduce amplitude of pulses
    - TIR takes place at core-cladding boundary
    - light would cross between touching fibres if there was no cladding
    - core must be narrow to prevent modal dispersion (different path lengths otherwise)
    - material dispersion from different wavelengths eg white light
    - endoscopes must use coherent bundles so image stays the same
- 5.4 Double slit interference
  - Young's double slit experiment
    - two slits act as coherent sources of waves meaning they emit light waves with a constant phase difference and ∴ same frequency
    - bright fringe - reinforcement (in phase)
    - dark fringe - cancellation (π out of phase)
    - fringes formed due to interference
    - fringe separation, w=(λD/s
  - The theory of the double slit equation
    - derived from diagram below
- 5.5 More about interference
  - Coherence
    - sources that emit light waves of the same frequency with a constant phase difference
    - doubles slits are coherent provided illuminate double slits with laser light, or with light from a narrow single slit if using a non-laser light
  - Wavelength and colour
    - longer wavelength = larger fringe separation
  - Light sources
    - vapour lamps and discharge tubes produce light with a dominant colour
    - light from a filament lamp of from the Sun has a continuous spectrum
    - light from a laser is:
      - coherent
      - highly monochromatic (can specify wavelength to within a nanometre)
      - never look along a laser beam, even after reflection
  - White light fringes
    - continuous spectrum
    - white central fringe
    - red diffracts more than blue so further out
- 5.6 Diffraction
  - Observing diffraction
    - water in a ripple tank
      - more spreading if narrower gap or longer wavelength
    - single slit
      - central fringe twice as wide as outer fringes and much more intense
  - More about single slit diffraction
    - width of central fringe, W=λ/a x 2D
      - a is width of the single slit
  - Single slit diffraction and Young's fringes
- 5.7 The diffraction grating
  - Testing a diffraction grating
    - a diffraction grating consists of a plate with many closely spaced parallel slits ruled on it
    - when beam of monochromatic light directed at diffraction grating, light is transmitted by the grating in certain directions only because:
      - light passing through each slit is diffracted
      - diffracted light waves from adjacent slits will either reinforce or cancel each other depending on the direction
    - central beam is in same direction as incident beam as is known as the zero order beam
  - The diffraction grating equation
    - dsinϑ=nλ
      - d=1/no. of slits per metre
      - round n down when calculating max. no. of orders
  - Types of spectra
    - continuous
      - eg from a filament lamp
    - line emission
      - glowing gas in vapour lamp or a discharge tube emits light at specific wavelengths so spectrum consists of narrow vertical lines of different colours
        wavelengths of lines characteristic of chemical element producing light
    - line absorption
      - continuous spectrum with narrow dark lines at certain wavelengths
        eg spectrum of light from filament lamp after passing through a glowing gas