Question

A transparent thin plate of polaroid is placed on another similar plate such that the angle between their axes is $30^{\circ}$. The ratio of the intensities of the emergent light and the unpolarised incident light will be
1. 1:3
2. 3:4
3. 3:8
4. 1:4

Answer 1

Hint: To solve this problem,we will use the mathematical form of law of Malus. Here a transparent thin plate is placed on another plate and it makes an angle $30^{\circ}$ with the axis of another plate. We have to apply the law of Maths and find the ratio of emergent light and the unpolarised incident light

Formula used:
If the electric field vector of light makes an angle $\theta$ with the transmission axis, then intensity of transmitted light is given by equation:
$I={{I}_{o}}{{\cos }^{2}}\theta $
where $I_0$ is the intensity of unpolarized light.

Complete answer:
We know that the law of Malus states that: If a linearly polarised light incident on a polaroid with electric field vector parallel to the transmission axis, then the light is completely transmitted by the polarizer. If they are perpendicular to each other then the light is stopped by the polaroid.

Thus, if the electric field vector of light makes an angle $\theta$ with the transmission axis, then intensity of transmitted light is given by equation:
$I={{I}_{o}}{{\cos }^{2}}\theta $
where $I_0$ is the intensity of unpolarized light.

Here in this question on applying Malus law, we get
$I=\frac{{{I}_{o}}}{2}{{\cos }^{2}}30{}^\circ $

That is the ratio between emergent and unpolarized light is:
$\frac{I}{{{I}_{o}}}=\dfrac{3}{8}$

Therefore, the answer is (C)

Additional Information:
For light waves, the direction of the electric field is fixed but its magnitude varies sinusoidally. If the electric field at a point is always parallel to a fixed direction as time passes, the light is called linearly polarised along that direction. The plane containing the electric field and the direction of propagation is called the plane of polarisation. If the resultant electric field has random direction, then the light waves are called unpolarized. The light from mercury lamp, electric tube, candle and light from sun are examples of unpolarized lights.

Polarizer is an instrument to produce polarised light from unpolarized light. There are many types of polarizers available today. Polaroid is one such instrument. They transmit light with an electric field vector parallel to a special direction.

Note: Here intensity gets half because two polaroids are kept parallel to each other. Also, there are different kinds of polaroids available today and not only does linearly polarised light exist but also circularly polarised and elliptically polarised light exists.