Waves

Oscillation of particles, that require a medium to travel

Oscillations of fields, that do not require a medium to travel

The direction of oscillations are parallel to the direction of energy transfer

The direction of oscillations are perpendicular to the direction of energy transfer

The process of forcing a transverse wave’s oscillations to one plane only.

Oscillations can change from one plane to another

It only allows light through that oscillates in a certain plane and direction - hence polarises it.

Crossed suggests that the 2 filters are at an angle of 90* to each other. When light passes through the first filter, the particles are polarised, and are not at 90* to the direction of the plane that the second filter polarises through. Therefore, the light cannot pass through the second filter, and the light intensity reduces to a minimum.

They reduce the glare of reflected light from the sun, by containing a polaroid filter, which polarises light to a specific plane, and reduces the light intensity.

distance and direction from equilibrium position

the maximum displacement

the smallest distance between 2 adjacent vibrating particles with same displacement and velocity

one max displacement to the next max displacement

time for one complete wave to pass a fixed point

number of complete waves passing a point per second

It is small

the fraction of a cycle it has completed since the start of the cycle

fraction of a cycle between the two particles

360* or 2π

2πd/λ

when two waves meet, the total displacement at a point is equal to the sums of the individual displacements at that point. They have to be travelling in opposite directions.

• crest + crest = supercrest (reinforcement)

• trough + trough =supertrough (reinforcement)

• crest + trough (of same amplitude) = minimum (cancellation)

When waves pass through each other at a constant frequency and phase difference, and cancellation/reinforcement occurs in fixed positions.

They produce an interference pattern when they overlap, because they vibrate at the same frequency and a constant phase difference.

The points of cancellation and reinforcement would change at random, so the interference pattern would not be seen.

A progressive wave is produced at one end of a string. A wave reflects back, and these 2 waves are travelling in opposite directions, with the same frequency. When they meet, they superpose and interfere constructively at antinodes and destructively at nodes (max displacement at antinodes, and minimum at nodes). Important to note that these nodes are at fixed points along the wave.

A point of minimum displacement, and hence 0 energy

A point of maximum displacement, and hence maximum energy

It is a wave on a string that vibrates at the fundamental frequency. It contains 2 nodes, and 1 antinode. The Length is equal to half lambda. The frequency is equal to the speed divided by 2 x the length.

We increase the frequency by 2x, and therefore half the total wavelength

At nodes, the amplitude of vibration is 0. At antinodes, the amplitude of vibration is maximum. These points are in fixed positions, therefore no energy can be transferred.

In stationary, all the particles vibrate at the same frequency, except those at nodes - in progressive, all particles vibrate at the same frequency no matter its position.

In stationary, amplitude varies from 0 at nodes, to maximum at antinodes - in progressive, all particles have the same amplitude.

In stationary, phase difference is equal to mπ, where m is the number of nodes between the 2 particles - in progressive, phase difference is equal to 2πd/λ.

The lowest frequency that produces an interference pattern on a stationary wave.

It consists of 3 nodes, and 2 antinodes.

L = λ

f = c/L

It consists of 4 nodes, and 3 antinodes.

L = 3λ/2

f = 3C/2L

Second harmonic frequency = 2 x first harmonic

Third harmonic frequency = 3 x first harmonic

L = mλ/2 (where m is the number of nodes in the portion of vibrating string)

High frequency = high pitch

Low frequency = low pitch

Increase pitch - increase tension/shorten length

Decrease pitch - decrease tension/increase length

It is the mass per unit length of the string

It is the change in direction that occurs when light passes at an angle across a boundary between 2 transparent surfaces

The ray bends towards normal - slows down (because air is less dense, and glass is more dense)

The ray bends away from normal - speeds up (because its moving from a dense medium to a less dense medium)

• air = 3×10^8

• glass = 2×10^8

The ray slows down, (the wavelength decreases), and so it bends towards the normal

The ray speeds up, (the wavelength increases), and so it bends away from the normal

• Angle of refraction is always less than angle of incidence.

• Partial reflection also occurs.

n1sinθ1 = n2sinθ2

The ratio between speed of light in a vacuum to speed of light in a material - always greater than 1, as no material is less optically dense than a vacuum

The ratio between the speed of light in one material compared to the speed of light in another - can be greater than 1

The speed of light in each substance (so the smaller the speed of light in a substance, the greater the refractive index of the substance because Ns = C/Cs)

The frequency of the wave DOES NOT CHANGE when refraction occurs, but the wavelength does. so Ns = λ/λs (where λs is the wavelength of the wave in the substance).

1 (1.0003)

White light is a combination of all the different wavelengths of visible light - spanning from red (650nm) - violet (350nm).

Dispersion happens due to the refraction of white light. The prism refracts the light at different amounts depending on the wavelength. The Shorter the Wavelength (in air) the greater the refraction, so each colour is diffracted by a different amount, and the speed of light in glass depends on wavelength (slower = lower wavelength = greater refraction).

It refracts across the boundary of the glass at 90* to the normal (and there is still some partial reflection - as partial reflection always occurs when the angle of incidence is less than or equal to the critical angle)

Then the ray undergoes total internal reflection (same as reflection of a mirror)

The incident substance should have a larger refractive index than the other substance

The angle of incidence should be greater than the critical angle

• Light enters diamond - splits into the colours of the spectrum

• Very high refractive index, so the colours are separated a lot

• Because of the high refractive index, the ray of light undergoes total internal reflection many times before it emerges from the diamond

• so the colours disperse more and more, and the diamond sparkles with many colours

A light ray is totally internally reflected each time it reaches the fibre boundary, because the angle of incidence exceeds the critical angle of the fibre. It might not reflect totally if the radius of the bend of the fibre is too small.

Pulses of light enter from one end at a transmitter, and reach a receiver at the other end.

• Fibres need to be highly transparent to avoid the absorption of light (absorption can continuously reduce the amplitude of the light)

• Each fibre consists of a core surrounded by a layer of cladding. The cladding has a lower refractive index to reduce light loss from the core (as this could reduce the amplitude of the light pulses)

Total Internal Reflection takes place at the core-cladding boundary. If there was no cladding, the light would cross from one fibre to the other if 2 fibres are in contact - signals would corrupt and be insecure, as would reach the wrong destination.

The core should be narrow to prevent modal (multipath) dispersion - it happens in a wide core because the light travelling along the axis of the core travels a shorter distance per metre of fibre compared to a ray that is repeatedly totally internally reflected. Also, a pulse of light sent via a wide core would become longer than it was supposed to be, and if it is too long, it may merge with the next pulse

Material/spectral dispersion. Occurs if white light is used instead of monochromatic light. (the speed of light in the optical fibre depends on the wavelength of light. Violet travels slower than red in glass, and so the difference in speed causes the white light pulses to become longer - as the violet component falls behind the red component - so we must use monochromatic light)

2 bundles

it is inserted into a body cavity, and illuminated using light sent through one of the bundles

A lens over the other bundle is used to form an image of the cavity on the end of the bundle - the light then travels in pulses to the other end of the bundle, where the image is observed. The bundle must be a coherent bundle.

Fibres at each end are in the same relative position.