Polarisation and Dispersion Revision Notes for Leaving Cert Physics

Polarisation and Dispersion

What is polarisation?

Light is a transverse electromagnetic wave, which means it vibrates perpendicular to the direction it travels. When light vibrates in all possible directions, we call it unpolarised light. However, when light vibrates in only one plane, we say it is polarised or plane-polarised.

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Polarised light is light with waves that are vibrating in one plane only.

When a filament light bulb produces light, electrons in the filament create electromagnetic waves that vibrate in many different directions. This makes the light unpolarised because the electric field vectors are vibrating in many different planes simultaneously.

How polarising filters work

Polarising filters are special materials that can control which direction light waves can pass through. Think of them like a fence with vertical slats - only waves vibrating vertically can pass through.

When unpolarised light hits a polarising filter, only the light waves vibrating in one particular direction can pass through. The filter blocks all the waves vibrating in other directions. This process transforms unpolarised light into polarised light.

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Key principle: If you place two polarising filters at right angles to each other (perpendicular), ideally no light gets through the second filter. This happens because the first filter only lets through vertically polarised light, but the second filter only allows horizontally polarised light to pass - since there's no horizontally polarised light left, no light gets through.

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This demonstrates that light behaves as a transverse wave, because only transverse waves can be polarised in this way.

Polarisation by reflection

When light reflects off glass, water, or other surfaces, the reflected light becomes partially plane-polarised. This means that reflected light has more waves vibrating in one direction than in others.

Polaroid filters take advantage of this property. These are materials that only allow light vibrating in one direction to pass through, effectively blocking much of the reflected light.

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Practical Applications of Polarising Filters:

Polaroid sunglasses reduce glare by blocking horizontally polarised reflected light
Camera filters can reduce reflections from windows and water surfaces
Car windscreens sometimes use polarising filters to reduce glare

When you hold a piece of polaroid material in front of polaroid sunglasses and rotate it by 90°, ideally no light gets through because the two polarising directions are perpendicular to each other.

Dispersion

Dispersion is the process where white light gets separated into its component colours. This happens because different wavelengths (colours) of light are refracted by different amounts when passing through materials.

Dispersion using prisms

When white light passes through a triangular glass prism, it spreads out into a rainbow of colours. This occurs because the refractive index of glass varies slightly for different wavelengths.

The refractive index is different for each wavelength, so each colour is refracted through a different angle. Red light is refracted the least and violet light is refracted the most. This is why red appears at one end of the spectrum and violet at the other.

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Important: When light is dispersed by a prism, red is refracted the least and violet the most. This creates the familiar rainbow pattern we see.

You can recombine the dispersed colours back into white light using a second prism positioned upside down relative to the first one.

We can observe this same effect in nature when sunlight passes through water droplets in the atmosphere, creating rainbows after rain showers.

Dispersion using diffraction gratings

A diffraction grating consists of many thousands of parallel lines ruled very close together (typically 400-600 lines per millimetre). When white light passes through a diffraction grating, it creates multiple spectra (orders) at different angles.

The grating equation helps us calculate the angles at which different colours appear:

$d \sin θ = nλ$

Where:

$d$ = spacing between grating lines
$θ$ = angle of diffraction
$n$ = order of diffraction (1, 2, 3...)
$λ$ = wavelength of light

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Worked Example: Calculating Diffraction Angles

For a diffraction grating with 400 lines per mm:

$d = \frac{1}{400} \text{ mm} = 2.5 × 10^{-6} \text{ m}$

For violet light ( $λ = 3.8 × 10^{-7}$ m) in the first order ( $n = 1$ ): $\sin θ = \frac{nλ}{d} = \frac{1 × 3.8 × 10^{-7}}{2.5 × 10^{-6}} = 0.152$ $θ = \sin^{-1}(0.152) = 8.7°$

For red light ( $λ = 7.0 × 10^{-7}$ m): $\sin θ = \frac{1 × 7.0 × 10^{-7}}{2.5 × 10^{-6}} = 0.28$ $θ = \sin^{-1}(0.28) = 16.3°$

This shows that red light deviates more than violet when dispersed by a diffraction grating, which is opposite to what happens with a prism.

Key differences between prism and grating dispersion

Property	Prism Dispersion	Grating Dispersion
Red light deviation	Least deviation	Most deviation
Violet light deviation	Most deviation	Least deviation
Number of spectra	One spectrum	Multiple spectra (orders)
Brightness	Bright spectrum	Dimmer but purer spectra

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Key Points to Remember:

Polarised light vibrates in one plane only, while unpolarised light vibrates in all directions
Polarising filters only allow light vibrating in one specific direction to pass through
When two polarising filters are perpendicular, no light gets through - this demonstrates light is a transverse wave
Dispersion separates white light into its component colours due to different refractive indices
With prisms: red bends least, violet bends most
With diffraction gratings: red deviates most, violet deviates least
The grating equation $d \sin θ = nλ$ helps calculate diffraction angles for different wavelengths

Polarisation and Dispersion (Leaving Cert Physics): Revision Notes