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Question

Distinguish between polarised and unpolarised light. Does the intensity of polarised light emitted by a Polarised depend on its orientation? Explain briefly.
The vibrations in a beam of polarised light make an angle of $$60^0$$ with the axis of the polaroid sheet. What percentage of light is transmitted through the sheet?


Solution

A light which has vibrations in all directions in a plane perpendicular to the direction of propagation is said to be unpolarised light. The light from the sun, an incandescent bulb or a candle is unpolarised. 
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 polarised or linearly polarised light. 
Yes, the intensity of polarised light emitted by a Polaroid depends on orientation of Polaroid. When polarised light is incident on a Polaroid, the resultant intensity of transmitted light varies directly as the square of the cosine of the angle between polarisation direction of light and the axis of the Polaroid. 
$$I \propto \ cos^2 \theta$$ or $$I = I_0 \ cos^2 \theta$$
Where $$I_0$$ = maximum intensity of transmitted light;
 $$\theta$$ = angle between vibrations in light and axis of Polaroid sheet. 
or, $$I = I_0 \ cos^2 \ 60^0 = \frac{I_0}{4}$$
Percentage of light transmitted = $$\frac{I}{I_0} \times 100 = \frac{1}{4} \times 100 = 25 \%$$

Physics

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