Question

(a) What is plane polarised light? Two polaroid sare placed at `90^(@)` to each other and the transmitted intensity is zero. What happens when one more polaroid is placed between these two, bisecting the angle between them? How will the intensity of transmitted light vary on further rotating the third polaroid?
(b) If a light beam shows no intensity variation when transmitted through a polaroid which is rotated, does it mean that the light is un-polarised? Explain briefly.

Answer 1

(a) Plane polarised light : When unpolarised light is passed through a tourmaline crystal cut with its face parallel to its crystallographic axis AB. Only those vibrations of light pass through the crystal, which are parallel to AB. All other vibrations are absorbed. The emerged light from the crystal is said to be plane polarised light.
If E is the amplitude of electric field component emanating from Ist polaroid then from 2nd polaroid at `45^(@)`.
The amplitude of electric field component is `E_(1)=E cos 45^(@) = E xx (1)/(sqrt(2))=(E)/(sqrt(2))`.
Again amplitude of electric field component coming from 3rd polaroid at `45^(@)` to 2nd polaroid would be
`E_(2)=E_(1) cos 45^(@)=(E)/(sqrt(2)).(1)/(sqrt(2))=(E)/(2)`= half of E
As intensity `alpha E^(2)`,
`:.` Intensity transmitted from three polaroids will be `(1)/(4)`th of the intensity transmitted from the first polaroid.
(b) No. The light which is made up of electric field components Ex, Ey with `90^(@)` phase difference but equal amplitudes. The tip of electric vector executes uniform circular motion at the frequency of the light itself.
When such light is passed through a polaroid, which is rotated, the transmitted average intensity remains constant.