Intensity and polarisationEdexcel A-Level Physics: Revision notes

When a wave transfers energy, we can describe how concentrated that energy is. The intensity I of a wave is the power incident per unit area, measured perpendicular to the direction of travel of the wave:

I = P/A

Intensity is measured in W m⁻², which in base units is kg s⁻³. If the power P is spread over a larger area, the intensity is lower.

Two useful consequences: for the same intensity, doubling the area doubles the power collected (this is why solar panels and radio dishes are large), and for a given area, a higher intensity delivers more power.

A point source radiating uniformly in all directions spreads its power over a sphere. At distance r the sphere has area 4πr², so

I = P/(4πr²)

This gives the inverse square law: intensity is proportional to 1/r². Doubling the distance cuts the intensity to one quarter, and tripling it cuts the intensity to one ninth.

The law assumes the source radiates equally in all directions and that no energy is absorbed on the way.

The intensity of sunlight on a panel of area 1.6 m² is 1000 W m⁻². Find the incident power, and the electrical output if the efficiency is 18%.

Incident power P = IA = 1000 × 1.6 = 1600 W

Electrical power = 0.18 × 1600 = 288 W

A panel of lower efficiency, 15%, must have a larger area to give the same output: incident power needed = 288 ÷ 0.15 = 1920 W, so A = 1920 ÷ 1000 = 1.9 m².

A transverse wave can oscillate in any direction perpendicular to its travel. An unpolarised wave has oscillations in all these directions. In a plane polarised wave the oscillations are restricted to one plane only.

A polarising filter has a transmission axis. It passes oscillations parallel to that axis and blocks those perpendicular to it. Light passing through is then plane polarised.

Only transverse waves can be polarised. Longitudinal waves, such as sound, oscillate along the direction of travel, so there is no perpendicular plane to restrict. The fact that light and radio waves can be polarised is evidence that they are transverse.

Radio and microwaves: a transmitter rod emits waves polarised parallel to the rod. A receiving rod gives maximum signal when parallel to the transmitter and almost none when perpendicular. Rotating the receiver through 360° gives two maxima and two minima.

Light: rotating a second filter (the analyser) in front of a first one varies the light transmitted from a maximum to almost zero.

Uses: polarising sunglasses reduce glare, because light reflected from water or roads is partly polarised horizontally and the lenses have a vertical transmission axis. Tilting the head 90° makes the glare return. Television aerials are fixed in the same orientation as the transmitter.