Polarisation
Sunglasses that cut glare
- Polarising sunglasses block the glare off water and roads.
- Rotate them and the brightness changes — even though the scene hasn't.
- They work by letting light through in just one plane.
What polarisation is
- Polarisation means making a transverse wave vibrate in one plane only.
- A polarising filter passes the part lined up with its axis and blocks the rest.
Polarising a transverse wave means making it vibrate:
A polarising filter passes only the vibration lined up with its axis, leaving the wave in a single plane.
Only transverse waves
- A transverse wave has many planes to choose from, so it can be polarised.
- A longitudinal wave (sound) vibrates along the travel — there is no other plane, so it cannot.
- So: if a wave can be polarised, it must be transverse.
Sound waves can be polarised.
No — sound is longitudinal (it vibrates along the travel), so there is no other plane to pick out.
If a wave can be polarised, it must be ____.
Only transverse waves have vibration directions perpendicular to travel, so only they can be polarised.
Malus's law
- Through a filter at angle $\theta$ to the polarisation: $I = I_0\cos^{2}\theta$.
- $\theta = 0^{\circ}$: all passes. $\theta = 90^{\circ}$: all blocked.
Polarised light of intensity $100\ \dfrac{\text{W}}{\text{m}^2}$ meets a filter at $60^{\circ}$ to its plane. What intensity gets through?
$I = I_0\cos^{2}\theta = 100 \times \cos^{2}60^{\circ} = 100 \times 0.25 = 25\ \dfrac{\text{W}}{\text{m}^2}$.
Worked example
- Polarised light of intensity $I_0$ meets a filter at $\theta = 60^{\circ}$.
- $I = I_0\cos^{2}60^{\circ} = I_0 \times (0.5)^{2} = \dfrac{I_0}{4}$.
- Two crossed filters ($90^{\circ}$) let through nothing at all.
Two polarising filters are crossed at $90^{\circ}$. How much light gets through?
$I = I_0\cos^{2}90^{\circ} = 0$ — crossed filters block the light completely.
You've got it
- polarisation = vibrating in one plane; only transverse waves can do it
- it is a test: if it can be polarised, it must be transverse (sound cannot)
- Malus's law: $I = I_0\cos^{2}\theta$ (crossed filters block all light)