^Sun appears red at Sun rise & sun set

This is because at Sun rise & sun set light passes through greater thickness of atmosphere, as a result more scattering takes place & blue colour & low wavelengths are scattered away by the scattering caused by the atmosphere & the colour which reaches us is unscattered red.

General scattering

When size of obstacles encountered by the light is much greater than the wavelength of light used, all wavelengths of light are scattered equally.

^Scattering of light

When unpolarized light falls on a gas or air molecules light falling on air molecules. The electric field of light polarises the air molecule makes it an electric dipole, which starts oscillating under the influence of oscillatory electric field of light & these dipoles radiate electromagnetic waves in all directions. This process is called scattering of light & the radiated light is called scattered light, it is unpolarized & intensity is found to be strongest along a line perpendicular to the oscillation, & drops to zero along the line of oscillation. The amount of scattering depends on the obstacle size coming in its way e.g. dust particles, rain drops, ice particles etc. We have divided scattering in two type.

1. Rayleigh scattering

When size of obstacles encountered by the light is much smaller than the wavelength (a << λ) of light used, the amount of scattering is inversally proportional to the fourth power of the wavelength of light.

^Malus law

Let I₀ be the intensity and ‘A’ the amplitude of the unpolarized light falling on the polarizer & θ be the angle between the pass axis of the polaroid & amplitude vector, then the component Acosθ, parallel to the pass axis (y) of polarizer passes through it & the component Asinθ, perpendicular to pass axis is blocked by the polarizer, thus the intensity of light transmitted by the polarizer is

I = k (A cosθ)² = k A² cos² θ

or         I = I₀ cos² θ        [called Malus law

Actually the phase angle for a beam of unpolarised light can have any value from 0⁰ to 360⁰. Now as the average value of cos² θ for the range 0⁰ to 360⁰ is 0.5, thus the average intensity of light transmitted by a polarizer is only 0.5 I₀.  Following observations can be explained on the basis of Malus law.

1. Two polarizes with parallel pass axis (y & y)

2. Two polarizes with crossed pass axis (y & z)

^How do polarisers work 

A Polaroid is a thin commercial sheet containing long chain of hydrocarbons which become conducting at optical frequencies & absorb the electric field parallel to chains & transmit the electric field perpendicular to the chain length. This is why a direction perpendicular to the chain length is called the transmission axis or pass axis of the polarizer. For shown drawing y axis is pass axis.

^Plane polarized light

If the electric field vector of a light wave vibrates just in one direction perpendicular to the direction of wave propagation, then it is said to be linearly polarized along that direction. Human eyes can’t distinguish between an unpolarised light and a polarized light, but the eyes of a bee can.