Question

What is the law of Malus? A plane polarized light of intensity 16 watt/m², is incident on a polaroid in such a way that the vibration of its electric vector makes an angle of 30° from the transmission axis of the polaroid. Find out the intensity of the transmitted light from the polaroid. Write down any one use of polaroid.

Hint:

Malus's law: \(I = I_0\cos^2\theta\). Put \(I_0=16\) and \(\theta=30^\circ\) with \(\cos^2 30^\circ = 3/4\).

Answer 1

Step 1 (State the rule): Malus's law describes how a polaroid dims polarized light. If the electric vector of the incoming polarized beam makes angle \(\theta\) with the polaroid axis, only the component along the axis is passed. Since intensity goes as amplitude squared, and the passed amplitude is \(E_0\cos\theta\), the transmitted intensity is
\[ I = I_0\cos^2\theta. \]

Step 2 (List knowns): Incident intensity \(I_0 = 16\ \text{W/m}^2\); angle between vibration and axis \(\theta = 30^\circ\).

Step 3 (Insert the angle): Here \(\cos30^\circ = 0.866\), hence \(\cos^2 30^\circ = (0.866)^2 = 0.75 = \tfrac34\).

Step 4 (Final intensity):
\[ I = 16 \times 0.75 = 12\ \text{W/m}^2 \]
So one quarter of the intensity is blocked and three quarters passes through.
\[\boxed{I = 12\ \text{W/m}^2}\]

Step 5 (A use): Polaroids are used as analysers to detect and measure the polarization of light; everyday examples include anti-glare sunglasses and camera polarizing filters.