According to Brewster’s law, when the beam of light is incident on the surface of a transparent material at polarising angle then the reflected light is completely plane polarized having ibrations perpendicular to the plane of incidence. However, the transmitted light is not completely plane polarised. The intensity of the reflected beam is very weak as only 8% of the incident light is reflected at each reflection. Thus to increase the intensity of plane polarized reflected beam one should increase the number of reflections.
The light incident at the polarising angle on a pile of thin parallel placed plates placed one on top of the other separated by thin sheet of papers with a central aperture otherwise plates will make good contact with each other and would act practically as a single slab. Then at each reflection more of the component vibrations perpendicular to the plane of incidence are filtered out with the result that the transmitted light becomes richer and richer in plane polarised light having vibrations in the plane of incidence. The apparatus has generally ten thin plates at an angle of 32.5° with the axis of the wooden tube as shown in Figure 6.6.
Law of Malus: According to law of Malus, when a beam of completely plane polarised
lightis incident on an analyser, the intensity (I) of light transmitted through analyser varies directly as square of cosine of angle (8) between the plane of transmission of the analyser and
Mathematically, I γ cos2 θ
Let a be the amplitude of vibrations transmitted by the polariser, along OP. The plane of polariser OA makes an angle e with OP. Resolving amplitude of vibrations into rectangular
(i) a cos θ along OA parallel to plane of transmission of analyser
(ii) a sin θ along OB, perpendicular to plane of transmission of analyser.
As component transmitted through analyser is a cos e only, so intensity of transmitted
I γ(a cosθ)2
I =k a2 cos2 θ
I = I 0 cos 2 θ (k2 =I 0)
where 10 is intensity of light transmitted by polariser which is constant.
Note. When an unpolarised light is passed through a polariser, it get polarised. It can be
proved that intensity of polarised light is half of the intensity of unpolarised light.
1 pol=1/ 2 I
In unpolarized light, the vibrations are in all probable directions in a plane perpendicular
to the direction of propagation. So,
Using law of malus
I =I 0 cos 2 θ
I pol =I unpol x 1/2.