Question

(a) Using the phenomenon of polarization, show how transverse nature of light can be demonstrated.

(b) Two polaroids $P_1$ and $P_2$ are placed with their pass axes perpendicular to each other. Unpolarised light of intensity $I_0$ is incident on $P_1$. A third polaroid $P_3$ is kept in between $P_1$and $P_2$ such that its pass axis makes an angle of ${30}^{\circ }$ with that of $P_1$. Determine the intensity of light transmitted through $P_1,P_2$ and $P_3$.

Answer 1

(a) Suppose that an ordinary light is incident normally on a pair of crystals $C_1$ and $C_2$. When the incident ray of light passes through crystal $C_1$, it gets plane polarised in the direction perpendicular to the length of crystal. Now, we see that when the axis of two crystals are parallel, the intensity of the emerging light will be maximum. When the second crystal is placed perpendicular with respect to the first crystal, the intensity of light observed is zero. This is due to the fact that the electric field of the plane polarised light obtained from $C_1$ can vibrate only in one direction. Hence, when the axis of the crystal is perpendicular to its direction of vibration of electric field, it gets blocked. This shows the transverse nature of light.


(b) Intensity of light after falling on $P_1$.

$I^{\prime }=\frac{I_0}{2}$

Intensity of light after falling on $P_3$.

$I^{\prime \prime }=I^{\prime }co{s}^2\left(\theta \right)=\frac{I_0}{2}co{s}^2\left({30}^{\circ }\right)=\frac{3I_0}{8}[\because cos{30}^{\circ }=\frac{\sqrt{3}}{2}]$

Therefore, a light of intensity $\frac{3I_0}{8}$ will pass through the $P_3$, and the angle between $P_3$ and $P_2$ will be ${60}^{\circ }$ because of the condition given in the question.

Intensity of light after falling on $P_2$,

$I^{\prime \prime \prime }=I^{\prime \prime }co{s}^2{60}^{\circ }$

$I^{\prime \prime \prime }=\frac{3I_0}{8}co{s}^2\left({60}^{\circ }\right)=\frac{3I_0}{32}[\because cos{60}^{\circ }=\frac{1}{2}]$