Intensity of photons/ Incoming Light
The energy of photons, striking normally per unit area per unit time is called intensity of
wave.
Let N photons striking on a area A in time t such that the
direction of velocity of photons and normal to the surface
are inclined at angle then Acos
E0 h Energy of each photon
E Nh Total energy of photons striking on the area A
Nh nh
I= = , where,
At cos cos A
frequency of each photon
n number of photons striking on a unit area per unit time.
Icos
h = = mc2 = pc
n
Icos
p = momentum of each photon =
nc
Calculation of Radiant pressure and force on the surface
Case-I: Let the photons are completely absorbed by surface
psin F2
Photon
F1
Photon F2
p F1 Photon rest
pcos
FBD of surface FBD of photon
Just before Absorption Just after Absorption
At the time of Absorption
F1 = Change of component of momentum of photons perpendicular to surface per unit time
IA cos2 F Icos2
F1 nAp cos Radiant pressure due to absorption pa 1
c A c
F2 = Change of component of momentum of photons along the surface per unit time
IA cos sin
F2 nAp sin
c
Case-II: Let the photons are completely reflected by surface
psin Photon
F1
Photon F1
p pcos pcos
FBD of surface FBD of photon
Photon psin
Just before Absorption At the time of Absorption
Just after Absorption
F1 = Change of component of momentum of photons perpendicular to surface per unit time
2IA cos2 F 2Icos2
F1 2nAp cos Radiant pressure due to reflection pr 1
c A c
Let r be the reflection co-efficient of surface, so
Radiant pressure r pr 1 r pa
Note: If intensity and cos are constant, concept of projected area is useful.
