A 2013 experiment by Paul A. Williams and collaborators mounted a 25-mm dielectric mirror on a commercial force-restoration balance. Removing its pan-weight compensation spring allowed horizontal force sensing with a horizontal laser path. They measured mirror optical reflectance and varied incidence from about to . A 1071-nm laser, capable of 530 W, was switched at 0.1 Hz. Digitized mass-equivalent readings were converted to force using ; quadrature demodulation isolated the switched signal from drift. [ref]
Measurement calibration used a 20-g mass, with checks down to 1 mg. The optical forces lay below that checked range, limiting the accuracy claim. An angle scan tested the predicted cosine dependence at fixed intercepted power. Replacing the mirror with a carbon nanotube coated absorber increased absorbed power while reducing the predicted optical force; no modulation peak was detected. This bounded gas-heating artifacts under those conditions, rather than proving their universal absence. The fitted slope was about 7% below . Inferring laser power requires calibrated force, optical reflectance, radiometric absorptance and angle of incidence, with measurement uncertainty for each. [ref]
For normal incidence in vacuum, a uniform beam delivers energy to an illuminated surface area during time . A perfect absorber receives momentum , so force divided by surface area gives . A perfect stationary mirror sends the photons back with reversed momentum, so momentum conservation gives twice the normal transfer, . These are time-averaged pressures; the microscopic arrivals need not be uniform.
Figure 1.
Photon momentum transfer to an absorber and a mirror
. Original idealized normal-incidence diagram. Blue arrows show the incoming photon momentum; orange shows the reflected photon momentum. The green arrow is the momentum delivered to the receiver, not another outgoing photon. The mirror reverses the incoming momentum and therefore receives twice as much. Details.
For a stipulated model light intensity and the exact SI speed of light ,
These are computed predictions, not measured data or a universal sunlight value. If the beam fully covers a normally oriented surface area , the intercepted radiant flux is and the absorber's force is . Using the total source power would be wrong if only part of its beam reaches the receiver. The absorption prediction assumes complete photon absorption, while the reflection prediction assumes complete specular reflection; transmission, scattering of light and directed thermal photon emission require their own outgoing momentum accounting.
Measure the angle of incidence between the incoming path and the surface's normal line, with . There are two separate cosine factors. A fixed actual surface area intercepts only its projected area , so . Each incoming photon supplies normal momentum on absorption, or twice that on specular reflection. Thus, for radiometric absorptance and reflected power fraction ,
This model assumes transmitted light continues straight in the same medium and carries away its original momentum. It omits thermal recoil and assumes a stationary receiver. At , fixed beam light intensity therefore gives one quarter of the normal-incidence pressure. For fixed intercepted radiant flux , however, the normal force has only one cosine factor. Equivalently, if the given quantity is receiving-surface irradiance , then . The distinction matters when interpreting an experiment's angle scan. [ref]
Absorption also transfers a tangential momentum component at oblique incidence. It contributes a tangential force, rather than normal pressure. Ideal specular reflection preserves the tangential momentum component, so it transfers only normal momentum.