HL – Wave Phenomena

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Optically active substances

As a polaroid allows through only one plane of polarized light, if you want to rotate the plane of polarization you can add a sugar solution and this will rotate the plane of polarization.

These substances such as sugar solution are known as optically active substances.

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Natural Frequency vs. Forced oscillations

Natural Frequency is the frequency at which an object oscillates when there is no repeated external force or a continuous force. We can also say that the object is in free oscillation.

Forced oscillations take place when an external force is continuously applied to  to the original frequency to cause a change in the frequency of the oscillations. This can be related to the idea of having a driving frequency.

The amplitude of the forced oscillation depends on comparative values of the natural frequency and the driving frequency. In addition it also depends on the amount of damping present

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Damping

Damping is a dissipating force that is always in the opposite direction to the direction of motion of the oscillating particle. As work is being done against the dissipating force energy is lost. Since energy is proportional to the amplitude, the amplitude decreases exponentially with time.

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Polariser and Analyser

A polariser turns the unpolarised light to polarised light. An analyzer is basically the same as a polarizer but instead of taking in unpolarized light it takes in polarised light.

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Polarisation

Unpolarised light is vibrating in all directions perpendicular to the direction of travel. Polarised light is vibrating in 1 direction or 1 plane perpendicular to direction of travel.

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Polarisation by Reflection

Lights can also be polarised just by reflection. When a light wave is reflected off a surface, it will be partially polarised. Usually reflected light is only partially polarised (MOST vibrations happening parallel to surface), but at a specific angle, when the refracted ray is perpendicular to the reflected ray, total polarisation occurs. This angle is called Brewster’s Angle. When light is coming from air, bouncing off from another surface, the index of refraction of that surface will equal the tangent of the Brewster Angle, n=tanθ

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Resonance

Resonance is when the natural frequency of an object or system is equal to the driving frequency of an external source. As two objects or systems resonate, there is a large energy transfer as well as a great amplitude.

Resonance is useful in tuning radios and television sets. They do this by creating a circuit with a resonant frequency at the same frequency as the desired station. Resonance is not useful for structures such as bridges and buildings. If extreme vibrations at the bridge’s natural frequency occur, it can cause a bridge to sway and then collapse.

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Concentration

Solutions are optically active, meaning that they can change the plane of polarized light. Sugar solution is optically active.

The amount of rotation of the plane of polarization depends on the concentration of the solution itself. The more concentrated it is, the greater the angle of rotation.

The concentration of the solution can be determined by placing the solution between 2 polarizers. Keeping the first polarizer stationary and rotating the second polarizer until no light passes through (or until maximum intensity is achieved) will determine the solutions concentration.

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Stress Analysis

Some substances become optically active when put under stress. When glass, perspex, polythene and some other plastics are under stress they become doubly refractive. If they are viewed in white light between two crossed Polaroids, coloured fringes are seen around the regions of strain. This effect is called ‘photoelasticity’ and is used to analyse stresses in plastic models of various structures.

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LCD's

In an LCD, each pixel of the display is made of a liquid crystal.

Normally, these crystals rotate the plane of polarisation through 90°s. However, when a battery is connected across them, they do not.

Thus, if a crystal is placed in between two polarisers perpendicular to each other, the crystal will go dark when a battery is connected. This is as the plane of polarisation is unaltered, resulting in the same effect that would occur when two perpendicular polarizers were placed on top of each other.

 

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Malus' Law

When unpolarised passed through a polariser, it’s intensity is reduced by 50%. When this light passes through an analyser (second polariser), the reduction in intensity is dependent on the angle between the polarization planes of the first and second polarisers.

  • If they are perpendicular to each other, no light is transmitted.
  • If the difference in angle is = θ; such that 0<θ<90; some light will pass.

This is as the analyser will allow the component of the light through that has the same plane of polarisation as it.

This component is given by A0cos(θ)

I is proportional to A^2. If we let the original intensity of the light entering the analyser  = I0; the intensity of the light passing through will be given by I = I0cos^2(θ)

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