Question

Malu’s law for the polarization of the light is derived from the fact that an electromagnetic wave consists of an electric field vector and a magnetic field vector. The intensity of light, I, received at a point by a detector is related to the electric field,E, at that point. How are the intensity and electric field related?

Answer 1

We know from the definition of Poynting vector which says that the energy crossing per unit time per unit cross-sectional area , perpendicular to the area is given by:

where is the electric field and is the magnetic field, but with the usage of maxwell's equations we can also write

where represents the direction of motion of the wave. and "c" is the speed of the wave.

Using the first and second equation we get:

from the definition of the intensity of radiation which states "how much energy is crossing per unit time per unit cross-sectional area", the pointing vector is the same as the intensity of radiation.

In deriving the (3) equation I have used the property of electromagnetic waves which are transverse in nature and thus .

The average value of the intensity will be:

which is the required answer.