Radiation Pressure
Radiation Pressure :- Maxwell predicted that an electromagnetic wave carries momentum() and energy() and when this electromagnetic wave is absorbed/reflected by a surface, it would experience a force in a direction perpendicular to the surface. Maxwell’s prediction was confirmed in 1903 by Nichols and Hull by precisely measuring radiation pressures using a torsion balance.
Let us consider that a light of intensity I falls on a surface A, having absorption and reflection coefficient ‘a’ and ‘r’ and assuming no transmission. For calculating the force exerted by the beam on the surface, we consider following cases :-
CASE I :- Radiation pressure in case of complete absorption of radiation and no reflection i.e., a = 1, r = 0.
Initial momentum of the photon, (in downward direction)
Final momentum of photon = 0
Hence,
CASE II :- Radiation pressure in case of complete reflection of radiation and no absorption i.e., r = 1, a = 0.
CASE III :- Radiation pressure in case of partial reflection and partial absorption of radiation, i.e., o < r < 1 and a + r = 1
CASE IV :- Radiation Pressure in case of incidence of light beam at an angle θ on the surface
Initial momentum of photon (at an angle θ with the normal) =
Final momentum of photon = 0
Change in momentum of photon perpendicular to surface and upward =
Energy incident per unit time normal to surface(of area A) = IA cosθ
No. of photons incident per unit time (on area A) =
Total change in momentum of photons per unit time perpendicular to surface(of area A) and upward =
Total momentum imparted to the surface (of area A) per unit time and downward =
Force on the surface (F) = total change in momentum per unit time = (perpendicular to the surface & downward)
Radiation Pressure =
CASE (B) :- a = 0, r = 1
In this case total change in momentum of one photon perpendicular to surface and upward =
No. of photons incident per unit time (on area A) =
Total change in momentum of photons per unit time perpendicular to surface(of area A) and upward =
Total momentum imparted to the surface (of area A) per unit time and downward =
Force on the surface (F) = total change in momentum per unit time = (perpendicular to the surface & downward)
Radiation Pressure =
CASE (C) :- Partial reflection and partial absorption, i.e., o < r < 1 and a + r = 1
Change in momentum of reflected photon(perpendicular to surface and upward) =
Change in momentum of absorbed photon(perpendicular to surface and upward) =
No. of photons incident per unit time (on area A) =
No. of photons reflected per unit time =
No. of photon absorbed per unit time =
Force due to reflected photon,
(perpendicular to the surface & downward)
Force due to absorbed photon,
(perpendicular to the surface & downward)
Total Force,
Hence radiation pressure on the surface,
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