Robert Hooke postulated that the extension of a wire (e or Delta L) is proportional to the load of force.
For springs, k is used as the constant, which is called the Spring Stiffness or Spring Constant.
When plotting a graph of load against extension for a material (e.g. Metal Wire) in this case, a straight line relationship occur's up until the elastic limit, where the graph starts to curve, meaning the material has become permanently stretched.
A stretch can either be Elastic, or Plastic:
Elastic stretches means that the material returns to it's original shape after the load is removed.
Plastic stretches means that the material is permanently stretched, i.e. when the load is removed the atoms do not return to their original positions.
Strain and Stress
A Stress causes a Strain.
Tensile Stress is defined as the force applied divided by the cross-sectional area.
Hence Stress = F / A (Units Nm^-2 or Pa)
Tensile Strain is defined as the change in length (extension) divided by the original length.
Hence Strain = e / l (No Units)
A stress big enough to break a material is called the Breaking Stress
As strain increases stress increases up until the Ultimate Tensile Stress (UTS), from then on it decreases slowly until the material breaks.
The Young Modulus
The young modulus is Tensile Stress / Tensile Strain.
Therefore E = Strain / Stress = ( F / A ) / ( e / l )
Unit's = Nm^-2
Up to a point called the limit of proportionality, the tensile strain is proportional to the tensile stress. Hence below this point the Young's Modulus of the material is a constant.
Using a graph to find the Young's Modulus: The gradient of the graph (dy / dx) gives us Tensile Stress / Tensile Strain, hence the Young's Modulus.
Stress Energy (Energy Stored) can be calculated by:
Energy = 0.5 x Stress x Strain
A refractive index is the ratio of how much slower the speed of light is in the material compared with in a vacuum. (The refractive index in a vacuum being 1.)
To work out a refractive index: n = c / v ( c = 3.0 x 10^8 ms^-1)
The relative refractive index between two given materials is given by: V1 / V2
Therefore these two equations give us: Refractive Index of the Boundary = Ratio of the Refractive Indices. I.e.
1N2 = (N2) / (N1)
Snell's Law: N1 * Sin i = N2 * Sin r
Optical fibres use differing refractive indices of the Cladding and the Core to totally internally reflect the light passing down the cable. This means data can be transported much faster.
Superposition and Coherence
Superposition of two waves is the addition of them. I.e it occurs when two or more waves pass through each other.
Coherent Waves are two of the same frequency, similar amplitude and the same wavelength with a fixed phase difference.
Interference can be Constructive or Destructive: (Dealing with two coherent waves)
Constructive Interference is where a crest meets a crest to give double the displacement.
Destructive Interference is where a crest meets a trough to give nothing - the two waves cancel each other out.