Recap on All Summer Work(Physics) 2
Density and Uncertainty
A micrometer measures to 0.01mm
Vernier Callipers measure to 0.1mm
% Uncertainty = (Smallest measuring increment / reading) x 100
To combine uncertainties, we simply add the uncertainties of all variables which are not mathematical constants.
Viscosity
When a body falls or rises through a fluid, it experiences a drag which is dependent on the viscosity of the fluid.
Stokes Law states that (for simplicity) when a sphere falls through a viscous fluid, its velocity increases until terminal velocity is reached(resultant force is 0N)
At terminal velocity:
Viscous Drag = 6πηrv
Viscous Drag = 6 x π x Fluid Viscosity x Radius x Velocity
Snell's Law
Snell's Law states that Sin(incident angle) is proportional to Sin(refracted angle), the constant of proportionality is denoted by "n" and is known as the refractive index.
n = (Speed of the Wave in a Less Dense Medium/Speed of the Wave in a Denser Medium
During refraction, it is often the case that a small portion of the light will be reflected rather than refracted.
When a light ray enters a more optically dense medium, wavespeed decreases, wavelength decreases but frequency remains constant.
Total Internal Reflection
Refractive index = cosec(critical angle)
Polarisation
Unpolarised light can move at every angle in space on a given plane.
Malus' Law: Intensity = Initial intensity x Cos^2(θ)
When θ = pi/2 (analyser filter is rotated 2pi relative to the first filter).
Simple Circuits
Light intensity α amplitude^2
Light intensity = Power/Cross-sectional area
Rather than being a measure of energy transfers from electrical energy to other forms, EMF is the energy supplied to a circuit per unit charge.
The current flowing through a device depends on the p.d across it and its physical, internal properties. Internal resistance is caused by physical properties of a material; this cannot be removed from a cell (this inseparability is signified through dotted lines)
Mean Drift Velocity
When:
n = number of charge carriers
e = individual charge of each carrier
v = drift velocity
V = Volume = LA
Total charge able to move = nLAe
Time taken for charge to leave the wire = L/v
Overall current = Charge/time = nLAe/L/v = nAev
Resistivity
Resistance α Length of wire
Resistance α 1/Area
R = ρL/A
Where ρ is resistivity, measured in Ohm-Metres
Potential Dividers
V(in)/R(1) + R(2) = V(out)/R(2)
Diffraction
If a wave hits a slit of its wavelength, the wave's direction of travel is bent, causing it to spread out after the slit.
If there are multiple slits, diffracted waves will superimpose.
Huygens principle states that "Every point on a wavefront acts as a source of smaller, circular wavelets; the surface tangent to these wavelets can predict the future position of the wave.
A wavefront is an imaginary line joining points on a wave that are in phase.
During x-rays, crystalline materials can act like diffraction gratings. Single wavelength x-rays are fired through the material; different materials have different co-efficients of attenuation(μ)
X-ray process:
1) Filament heats up, electrons have enough energy to overcome the work function.
2) Electrons are repelled and accelerated by a negatively charged cathode.
3) Electrons are attracted to the anode, hitting it with great amounts of energy.
4) Electrons in anode excite then de-excite, emitting x-rays.
5) Because most of the electrons' energy is converted to heat, the tungsten anode has to be rotated.
Diffraction Gratings
dSin(θ) = nλ
Where n = order maxima
λ = Wavelength
d = Distance between slits
Bragg's equation concerns crystalline materials and their "layers" of diffraction gratings.
Bragg's equation: 2dSin(θ) = nλ
Electron Waves
Visible light microscopes are limited because of their high wavelength relative to those of the "specimen". Instead, higher frequency microscopes are used.
In 1923, De Broglie proposed that particles should also displace wave-like properties; the De Broglie wavelength of these particles "depends on its momentum": "λ = h/mv"
The diffraction pattern formed by electrons fired at a surface (multiple fringes) shows this wave-particle duality.
Every particle has a De Broglie wavelength but only, smaller, less-massive ones have a substantial wavelength.
Electron Guns
- Electrons are accelerated through a positively charged electrode grating by a negatively charged electrode.
- These electrode have a P.D: V = E/Q.
- 1/2mv^2 = eV
- Plugging into the De Broglie wavelength: λ = h/msqrt(2eV/m)
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