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How waves explain the behaviour of light Cheat Sheet by

Unit 4 AOS1 VCE Physics 2021

Formulas

f=1/T
v=fλ
λ=c/f
v=λ/T
constr­uctive p.d (antinode) =
'loud', 'light band'
or nλ = |S₁X-S₂X|
destru­ctive p.d (node) = (n-0.5)λ
'quiet', 'dark band'
or (n-0.5)λ = |S₁X-S₂X|
one free end, one fixed (odd):
λ=4L/n, f=nv/4L
fixed ends:
λ=2L/n, f=nv/2L
fringe spacing:
∆x=λL/d
bigger Δx gives more refrac­tion, more spread out
Δx=fringe spacing (m), λ=wave­length (m), L=distance from slits to screen (m), d=slit separation (m)
refraction & reflec­tion:
n=c/v
where; n=speed of light in a vacuum/ speed of light medium
n₁v₁=n₂v₂
diffra­cti­on∝λ/w
n₁sin(­θ₁)­=n₂­sin(θ₂)
energy­∝fr­equency
n₁sin(­θ₁)=n₂

Young's double slit experiment

Young’s double slit experiment shows light exhibiting the wave properties of diffra­ction and interf­erence.
Light can be polarised, observed as white light diffracts and colours are seen as a result. As only transverse waves can be polarised, the wave model of light is proven.

Snell's Law

n₁=ref­ractive index of first medium
θ₁=angle to the normal in first medium
n₂=ref­ractive index of second medium
θ₂=angle to the normal in second medium
 

Wave types

Transverse waves: particle moves along vertical axis
Longit­udinal waves: particle moves along horizontal axis
Coherent waves: waves with the same frequency
Mechanical (sound, air, water) waves do not exist in a vacuum, they require a medium to travel through
Electr­oma­gnetic (light) waves can exist in a vacuum, do not require a medium
Travelling wave: a wave for which the crests and troughs travel in the direction of wave propag­ation.
Standing Waves: when 2 wave trains with the same amplitude and wavelength move through each other, the resulting interf­­ering pattern results in a standing wave. Consists of altern­ating nodes and antinodes that remain in a fixed position, wave appears to be statio­nar­y/'­sta­nding'
fundam­ental frequency: n=1
formation of standing waves on a string:
1. waves reflect at both ends of string
2. reflec­tions travel in opposite directions with the same frequency and amplitude
3. fixed ends are nodes, free ends are antinodes

Nodes & Antinodes

Cons­t­r­­­uctive Interf­­­e­r­ence: When waves in the same phase overlap, their amplitudes add together
Dest­r­u­­­ctive Interf­­­e­r­ence: When waves of different phases overlap, their amplitudes cancel
Nodes: Points of complete destru­­­ctive interf­­­e­rence
Anti­n­od­es: Points of complete constr­­­u­ctive interf­­­e­r­ence, largest amplitude
 

Wave resonance

Waves reflect at the end of a string and are inverted if end is fixed
An object or system will resonate if driven at its natural frequency
Resonance greatly increases magnitude of oscill­ation in an object­/system

Doppler effect

Doppler effect is the detected frequency change due to the relative motion between a wave source and detector.
f increases when source and detector move towards each other
f decreases when source and detector move away from each other

Doppler effect:

Polarising filters

Waves

Variables

indepe­ndent: variable that is being changed (x-axis)
dependent: variable that is being measured (y-axis)
 

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