Question

Show that the radiation pressure exerted by an EM wave of intensity I on a surface kept in vacuum is I/c.

Answer 1

Let us consider a surface exposed to electromagnetic radiation. The radiation is falling normally on the surface. Further, intensity of radiation is I and area of surface exposed to radiation is A.

E = Energy received by surface per second = I.A

N = Number of photons received by surface per second

N = `E/E_("photon") = (Eλ)/(hc) = (IAλ)/(hc)`

Let the surface is perfectly absorbing, `ΔP_("one photon") = h/λ`

⇒ F = `N xx ΔP_("one photon") = (IA)/c`

Also, Pressure P = `F/A = I/c`