The wave nature of light was well established by the end of the nineteenth century because of the discoveries of phenomena like interference, diffraction and polarisation of light. But, the discovery of the photoelectric effect by Hertz is something which can not be proved by the wave nature of light and for that, we have to assume light as a particle.
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It was evident from the photoelectric effect that light possessed particle-like behaviour and it behaved as quanta or packets of energy upon interaction with matter.
Light or electromagnetic waves consist of a stream of tiny particles called photons.
Photons are the smallest possible packets of electromagnetic energy. A photon has a definite energy and momentum. Quantization of energy of light means that the energy of light is only available in integral multiples of which each packet of energy i.e. a photon possesses. This is known as quantum theory of light.
Where wavelength & frequency
Planck constant
The energy crossing per unit area per unit time perpendicular to the direction of propagation is known as Intensity of light(𝐼).
Where number of photons incident per sec
wavelength of light
Energy contained in one photon,
Energy incident per second,
Therefore, intensity
Photon count(𝑛): No. of photons emitted per second by a source.
Power of the source,
Since intensity of light,
Photon count,
Number of photons incident normally on a surface per second per unit area is known as photon flux. It is denoted by
The pressure experienced by the surface exposed to the radiation is called radiation pressure.
𝑃: Radiation pressure
𝐹: Normal force on plate due to photons
𝐴: Area of the plate
Complete absorption
Initial momentum of each photon,
Where, λ= wavelength of light
As, the photon is completely absorbed, the final momentum of each photon will be zero
The change in momentum of each photon,
Let be the no. of photons incident per second
Force acting on surface = Net change in momentum per second,
Since intensity,
Therefore net force,
Radiation pressure,
light is incident at an angle ,
Force acting in direction of momentum of photons,
Radiation pressure,
Complete reflection
Assumption:- The collision of photons with the surface is elastic
Initial momentum of each photon,
Where, λ= wavelength of light
As the photon is completely reflected and the collision is elastic, therefore the final momentum of each photon will be the same in magnitude and opposite in direction.
Final momentum of each photon,
The change in momentum of each photon,
Force acting on surface = Net change in momentum per second,
Since intensity,
Therefore net force,
Radiation pressure,
light is incident at an angle ,
Force acting in direction of momentum of photons,
Radiation pressure,
Partial absorption and partial reflection
Here, = absorption coefficient and, = reflection coefficient
If be the no. of photons incident per second
Then, number of photons absorbed per second,
and, number of photons reflected per second,
Radiation pressure due to absorption,
Radiation pressure due to reflection,
Net radiation pressure,
For complete reflection,
For complete absorption,
When light is incident at an angle ,
Radiation pressure due to absorption,
Radiation pressure due to reflection,
Net Radiation pressure,
Q 1. When the sun is directly overhead, the surface of the earth receives of sunlight. Assume that no light is absorbed in between the sun and the earth’s surface and the light is monochromatic with average wavelength 500 𝑛𝑚. The distance between the sun and the earth is . Find the number of photons falling per per second on the earth’s surface directly below the sun.
Answer:
Intensity of sunlight received by the surface of earth,
As, the sun is directly overhead, therefore the radiations falling on the earth are perpendicular to the surface of the earth.
Since intensity,
Q 2. A parallel beam of monochromatic light of wavelength is incident on a totally reflecting plane mirror. The angle of incidence is 60° and the number of photons striking the mirror per second is . Find the force experienced by the mirror due to the light beam.
Answer:
Therefore, Radiation pressure is given by,
As, the direction of force is perpendicular to the plane mirror
Therefore, force exerted by the light beam on the mirror is
Q 3. Figure below shows a light source having power P. The block being placed in the path experiences force due to light rays and we need to find this force. The surface of body on which the light beam is incident is having a reflection coefficient and absorption coefficient .
Answer:
Net radiation pressure,
Where = reflection coefficient
Force exerted on the block,
Q 4. A plane strip of mass 𝑚 suspended from a fixed support through a string. The string completely absorbs a horizontal continuous beam of monochromatic light. 𝑊 is the energy incident on the stripper unit. Find the deflection of the string from the vertical, if the strip stays in equilibrium.
Answer: Assumption: 𝛉 is very small
Therefore, this can be taken as the case of normal incidence of light beam
Hence, the Radiation pressure,
Therefore, force exerted by the light beam on the strip is
At equilibrium position, net force in horizontal and vertical direction is zero.
Therefore,
Dividing both equations,
Q 1. Does the number of photons remain conserved?
Answer: No. Because a particle can absorb a photon and take up its energy. Also an excited atom can go from one state to another and emit energy in the form of photons. That’s why the number. of photons may not be conserved.
Q 2. What are the dimensions of radiation pressure?
Answer:
Q 3. Which phenomena can be explained only by the wave nature of light?
Answer: Diffraction and interference.
Q 4. The energy and momentum of light are quantized. What does this statement mean?
Answer: Quantization means that the energy of light is only available in integral multiples of which each packet of energy i.e. a photon possesses.