A point source $\mathrm{S}$ emits unpolarized light uniformly in all directions. At two points $\mathrm{A}$…
A point source $\mathrm{S}$ emits unpolarized light uniformly in all directions. At two points $\mathrm{A}$ and $\mathrm{B}$, 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 $\mathrm{B}$, then the new value of $r$ will be ______
Solution
\(I \propto \frac{1}{l^2}\)
Where I: distance from point source.
\(\begin{aligned}
& \Rightarrow \frac{I_A}{I_B}=\frac{I_B^2}{I_A^2}=2 \\
& \Rightarrow I_B=\sqrt{2} I_A .
\end{aligned}\)
Also, due to polaroids:
\(\begin{aligned}
& I_B^{\prime}=\frac{I_B}{2} \cos ^2 45^{\circ}=\frac{I_B}{4} \\
& \Rightarrow I_B^{\prime}=\frac{I_B}{4} \ldots \text { (2) } \\
& \Rightarrow \text { Ratio becomes } 4 \text { times. } \\
& \Rightarrow r_{\text {new }}=8
\end{aligned}\)