question_answer

Two polaroids are placed in the path of unpolarised beam of intensity \[{{I}_{0}}\] such that no light is emitted from the second polaroid. If a third polaroid whose polarisation axis makes an angle \[\theta \] with the polaration axis of first polaroid, is placed between these polaroids, then the intensity of light emerging from the last polaroid will be :

A)  \[\left( \frac{{{I}_{0}}}{8} \right){{\sin }^{2}}(2\theta )\]          

B)  \[\left( \frac{{{I}_{0}}}{4} \right){{\sin }^{2}}(2\theta )\]

C)  \[\left( \frac{{{I}_{0}}}{2} \right){{\cos }^{4}}(\theta )\]                       

D)  \[{{I}_{0}}{{\cos }^{4}}(\theta )\]

Correct Answer: A

Solution :

Let initial intensity of light is \[{{I}_{0}}\] so, intensity of light after transmission from first polaroid \[=\frac{{{I}_{0}}}{2}\] Intensity of light emitted from \[{{P}_{3}}\] \[{{I}_{1}}=\frac{{{I}_{0}}}{2}\,{{\cos }^{2}}\theta \] Intensity of light transmitted from last polarized \[{{P}_{2}}={{I}_{1}}{{\cos }^{2}}\,({{90}^{0}}-\theta )\] \[{{P}_{2}}=\frac{{{I}_{0}}}{2}\,{{\cos }^{2}}\theta \,{{\sin }^{2}}\theta \] \[{{P}_{2}}=\frac{{{I}_{0}}}{8}\,{{(2\sin \theta \,\cos \theta )}^{2}}\] \[{{P}_{2}}=\frac{{{I}_{0}}}{8}\,{{\sin }^{2}}2\theta \]