A point source $S$ emits unpolarized light uniformly in all directions. At two points $A$ and $B$, t

Question

A point source $S$ emits unpolarized light uniformly in all directions. At two points $A$ and $B$, the ratio $r=I_{A} / I_{B}$ of the intensities of light is 2 . If a set of two polaroids having $45^{\circ}$ angle between their pass-axes is placed just before point $B$, then the new value of $r$ will be _______ .\

Professor PC Thomas Classes · Answer

(8) : Given, $r=I_{A} / I_{B}=2, 	heta=45^{\circ}$ As we know that intensity, $I \propto 1 / d^{2}$ Where $d$ is the distance from point source. $$\begin{equation*} 	herefore \frac{I_{A}}{I_{B}}=\left(\frac{d_{B}}{d_{A}}ight)^{2}=2 	ag{i} \end{equation*}$$ so, $d_{B}=\sqrt{2} d_{A}$\ According to Malus law,\ $I_{B}^{\prime}=\frac{I_{B}}{2} \cos ^{2} 45^{\circ}=I_{B} / 4$\ So, ratio becomes 4 times.\ Thus, $r^{\prime}=\frac{I_{A}}{I_{B}^{\prime}}=\frac{I_{A}}{I_{B}} 	imes 4=4 	imes 2=8$\