Question

If light intensity is known, how is non-reflecting momentum calculated?

Hint:

The momentum of non-reflecting light can be calculated using the energy flux divided by the speed of light.

Answer 1

Step 1: Understanding the formula.
The momentum \( p \) of light can be calculated using the energy flux \( U \) and the speed of light \( c \). The energy flux \( U \) is the energy transferred per unit area per unit time, and the speed of light is the constant \( c = 3 \times 10^8 \, \text{m/s} \).
Step 2: Formula derivation.
The relationship between momentum and energy flux is given by: \[ p = \frac{U}{c} \] This formula is used to find the momentum of non-reflecting light, where the energy flux \( U \) is divided by the speed of light \( c \).
Step 3: Conclusion.
Thus, the momentum \( p \) can be calculated using the above formula.

Answer 2

Step 1: Light carries momentum along with its energy.

Step 2: If U is the energy falling per unit area per unit time (energy flux), and c is the speed of light, the momentum is p = U ÷ c.

Step 3: So once you know the light's intensity (U), just divide it by the speed of light to get its momentum.

Answer 3

Via the photon energy-momentum relation.
For electromagnetic radiation, each photon's energy and momentum are linked by \( E = pc \), so momentum is energy divided by \( c \).
Summing this over all the photons striking a surface per unit area per unit time, the energy flux \( U \) converts to a momentum flux of \( p = U/c \).
For a surface that absorbs the light completely without reflecting it, this full amount \( U/c \) is delivered as momentum (a reflecting surface would instead receive twice this, \( 2U/c \), since the light's momentum reverses direction).