Radiation Pressure - Practice Questions & MCQ

Consider a point source of light emitting photons. And we want to find the number of Photons (n) emitted by this point source per second.

let the wavelength of light emitted by this =  and 

the power of the source as P (in Watt or J/s)

As we know the energy of each photon is given by 

where 

where c = Speed of light, h = Plank's constant = 

            = Frequency in Hz , = Wavelength of light. 

or we can write the energy of each photon as 

Then ( n=the number of photons emitted per second) is given as

The intensity of light (I) : The intensity of any quantity is defined as that quantity per unit area.

So here, light energy (or radiation ) crossing per unit area normally per second is called intensity of light energy (or radiation ).

And the intensity I is given as 

Its unit is  or 

The intensity of light due to a point isotropic source:

Isotropic source means it emits radiation uniformly in all directions.

So The intensity I due to a point isotropic source at a distance r from it is given as

The photon flux () is defined as the number of photons incident on a normal surface per second per unit area.

As we know  n ( the number of photons emitted per second) is given as

Similarly  intensity I is given as 

So The photon flux () is given as ratio of Intensity (I) to Energy of each photon

or  

• The photon flux () due to a point isotropic source:

The photon flux () due to a point isotropic source at a distance r from it is given as

Radiation pressure/force- When photons fall on a surface they exert a pressure/force on the surface. The pressure/force experienced by the surface exposed to the radiation is known as Radiation pressure/force.

As we know

n=Number of emitted photons per sec is given as 

where E= The energy of each photon

and Momentum of each photon is given as 

And we know the force is given as rate of change of momentum.

I.e For each photon 

and for n photons per sec 

For a black body, we get 100 % absorption or a=1

i.e for this surface 100% of the photon will be absorbed

so 

So Force is given as 

where P=Power

As 

So Force is given as 

and radiation pressure is given as 

• For perfectly reflecting surface (i.e mirror)

 i.e r=1

i.e  for this surface 100% of the photon will be reflected

i.e 

So 

So Force is given as 

and radiation pressure is given as 

• For neither perfectly reflecting nor perfectly absorbing body

i.e body having Absorption coefficient=a and reflection coefficient=r

and we have 

So Force is given as 

and radiation pressure is given as