Unpolarized light of intensity \(I\) is incident on a system of two polarizers, \(A\) followed by \(B.\) The intensity of emergent light is \(I/2.\) If a third polarizer \(C\) is placed between \(A\) and \(B,\) the intensity of emergent light is reduced to \(I/3 .\) The angle between the polarizers \(A\) and \(C\) is \(\theta \) . Then

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Correct Answer

(A) \(\cos \,\,\theta \, = \,{\left( {\frac{2}{3}} \right)^{1/4}}\)

Detailed explanation

Polariser \(A\) and \(B\) have same alignment of transmission axis. Lets assume polariser \(C\) is introduced at \(\theta \) angle

\(\frac{1}{2}{\cos ^2}\,\theta \, \times {\cos ^2}\,\theta \, = \,\frac{1}{3}\)

or, \({\cos ^4}\,\theta \,\, = \,\frac{2}{3}\, \Rightarrow \,\cos \,\theta \, = {\left( {\frac{2}{3}} \right)^{1/4}}\)

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