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 ___.

Answer 1

Correct answer is : 8

\(I \propto \frac{1}{l^{2}}\)

Where I : distance from point source.

\(\Rightarrow \frac{I_{A}}{I_{B}}=\frac{I_{B}^{2}}{I_{A}^{2}}=2 \)

\(\Rightarrow I_{B}=\sqrt{2} I_{A} \)  ...(1)

Also, due to polaroids:

\(I_B^{\prime}=\frac{I_B}{2} \cos ^2 45^{\circ}=\frac{I_B}{4}\)

\(\Rightarrow I_B^{\prime}=\frac{I_B}{4}\)  ...(2)

\(\Rightarrow\) Ratio becomes 4 times.

\(\Rightarrow r _ {new} = 8\)