Calculate photon energy without confusing it with power

Two quantities that a bright lamp can hide

A beam supplies energy over time; a photon carries an individual quantum of that energy. We can hold one quantity fixed while changing the other. In this original comparison, the wavelength is 500 nm and beam power is 2 mW. Neither value describes a real device or gives permission to illuminate an eye.

Convert 500 nm to 5×10⁻⁷ m. Frequency is c/λ≈5.996×10¹⁴ Hz. Multiplying by Planck’s constant gives E≈3.973×10⁻¹⁹ J per photon. Dividing by 1.602176634×10⁻¹⁹ J/eV gives about 2.480 eV. The unit conversion changes the numerical representation, not the energy.

Reconstruct the photon rate

Two milliwatts is 0.002 J/s. Divide this by energy per photon to obtain approximately 5.034×10¹⁵ photons/s. A larger number of photons is not a larger energy for each photon. Capture the result before changing a control, and write your predicted ratio for the next run.

At 4 mW with the same 500 nm wavelength, energy per photon stays 2.480 eV while photon rate doubles. At 250 nm and 2 mW, each photon has twice the original energy, so only half as many photons per second supply the same power. These relations depend on a monochromatic beam. A source with a distribution of wavelengths needs an energy-weighted calculation rather than one arbitrary wavelength.

Check a new beam

A 750 nm beam supplies 3 mW. Calculate energy per photon, photon rate and the ratio of photon rates compared with 500 nm at 2 mW. Show metres and watts before substituting.

Where the explanation applies

The model omits bandwidth, detector efficiency, reflection and absorption. It cannot infer tissue damage, detector counts or electrical output from beam power alone. Classical wave intensity remains useful for describing a beam’s average energy flow; the photon account is needed when an interaction transfers discrete energy. One representation does not make the other universally wrong.

Source and authorship

Reference for the physical relationship. Source checked 30 October 2026. The explanations, numerical cases, questions and diagrams here are original; reference material is not copied. Exact h,c,e follow NIST SI definitions.