^Appearance of sky

The appearance of sky from earth at various locations depend on the amount & nature of impurities present in the air & climatic conditions also.

Also it is found that the light scattered

(a) at right angles to the direction of incidence is completely plane polarized light (CPL)

(b) along the direction of incidence is unpolarized, &

(c) at all other angles to the direction of incidence is partially plane polarized light (PPL)

On the Moon, there is no blue sky because there is no atmosphere & thus no scattering. Even during the day, the sky is as black as at night, although the Sun and the Earth may be brightly shining.

If we look at the blue portion of the sky through a Polaroid and rotate the polariod, the transmitted light shows rise and fall of intensity, which indicates that the light from the blue portion of the sky is plane polarized.

^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.

^Brewster’s law

Brewster discovered that when ordinary light is incident on the surface of a transparent medium the reflected light is partially plane polarized.

The extent of polarization depends on the angle of incidence. For a particular angle of incidence (called polarizing or Brewster angle (i_p or p)

1. the reflected light is found to be completely polarized with its vibrations perpendicular to the plane of incidence.

2. the reflected & transmitted rays are perpendicular to each other, as shown in figure.

3. μ = tan p                           [called Brewster law

At i = p Ray 1: Incident ray (unpolarised)

Ray 2: Reflected ray (completely polarised)

Ray 3: Refracted ray (partially polarised)

For a ray incident form air to glass

^aμ_g = 3/2, so p = tan^-1  3/2  ⇒ p = 56.3⁰

For a ray incident form air to water

^aμ_w = 4/3,  so p = tan^-1  4/3 ⇒  p = 53.1⁰

^Light through a polarizer

Let ordinary light propagating along +x axis falls normally on a tourmaline crystal having pass axis parallel to y axis as shown in the following diagram.  On passing through the tourmaline crystal the electric field vibration parallel to pass axis are transmitted while the electric field vibration normal to pass axis are absorbed by the tourmaline.