Photon Intensity
Frequency controls the energy of each photon. Intensity measures how quickly energy crosses each square metre, so keep photon energy separate from photon arrival rate.
Intensity changes how many photons arrive
From AS Waves, power is the total energy transferred each second. Intensity is the power passing through each square metre of area normal to the beam.
Symbols
- = intensity of the beam (W m⁻²)
- = power of the whole beam (W)
- = cross-sectional area normal to the beam (m²)
First compare two beams with the same frequency. Their photons have the same energy. The higher-intensity beam transfers more energy through each square metre every second, so more photons must arrive through each square metre every second. The figure also keeps the beam area the same, so the higher-intensity beam has a greater total photon rate.
LOWER INTENSITY
same frequency · same beam area
same energy per photon
fewer photons per m² per s
HIGHER INTENSITY
same frequency · same beam area
same energy per photon
more photons per m² per s
- At fixed frequency, higher intensity means more photons per unit area per unit time.
- If the beam area is also fixed, higher intensity means more photons across the whole beam each second.
- Higher intensity does not give more energy to each photon. Only frequency sets that energy.
- If the same beam spreads over a larger area with no energy loss, its intensity decreases. The energy of each photon and the total number of photons per second do not change.
This distinction is assessed directly in photon questions (9702/41/M/J/21 Q12(a)) (9702/42/O/N/23 Q8(b)(ii)).
Worked example
Find total beam power from intensity
In (9702/43/O/N/23 Q8(b)(i)), a light beam has an intensity of 160 W m⁻² and a cross-sectional area of 2.5 × 10⁻⁶ m². Before finding its photon rate, find its total power.
Beam B has twice the intensity of beam A. Both beams have the same frequency and cross-sectional area. Compare their photon energy, the number arriving per unit area per unit time, and the total number arriving each second.
Show worked answer
The photon energy is the same because the frequency is the same. Beam B has twice as many photons arriving per unit area per unit time. Because the beam area is also the same, its total photon rate is twice as large.
Frequency sets the energy of each photon. At fixed frequency, intensity changes how many photons arrive per unit area per unit time.