Ncert Exercises & Solutions

Show that the radiation pressure exerted by an EM wave of intensity I on a surface kept in a vacuum is $\frac{I}{c} .$

Hint: The radiation pressure depends on the energy transferred to the surface.

Step 1: Find the momentum transferred.

Pressure = \frac{Force}{Area} = \frac{F}{A}

Force is the rate of change of momentum .

i . e ., F = \frac{dp}{dt}

Step 2 : Find the radiant pressure .

Energy in time dt, U = pc or p = \frac{U}{c}

∴ Pressure = \frac{1}{A} . \frac{U}{c . dt}

Pressure = \frac{I}{c} [∵ I = Intensity = \frac{U}{A . dt}]