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 (Law of Malus): When completely plane-polarized light of intensity \(I_0\) falls on a polaroid (analyser), the intensity of the transmitted light is proportional to the square of the cosine of the angle \(\theta\) between the light's plane of vibration and the transmission axis of the polaroid:
\[ I = I_0 \cos^2\theta \]

Step 2 (Given data): \(I_0 = 16\ \text{W/m}^2\), \(\theta = 30^\circ\).

Step 3 (Value of the cosine): \(\cos 30^\circ = \dfrac{\sqrt3}{2}\), so \(\cos^2 30^\circ = \dfrac{3}{4}\).

Step 4 (Substitute and compute):
\[ I = 16 \times \frac{3}{4} = 12\ \text{W/m}^2 \]
\[\boxed{I = 12\ \text{W/m}^2}\]

Step 5 (One use of polaroid): Polaroids are used in sunglasses to cut down glare from reflected light. (Other valid uses: to control light intensity in windows, in photographic filters, and in LCD screens.)