question_answer

Two Polaroids \[{{P}_{1}}\] and \[{{P}_{2}}\] are placed with their axis perpendicular to each other. Unpolarised light \[{{I}_{0}}\] is incident on \[{{P}_{1}}\]. A third polaroid \[{{P}_{3}}\] is kept in between \[{{P}_{1}}\] and \[{{P}_{2}}\] such that its axis makes an angle \[45{}^\circ \] with that of \[{{P}_{1}}\]. The intensity of transmitted light through \[{{P}_{2}}\] is

A) \[\frac{{{I}_{0}}}{4}\]

B)        \[\frac{{{I}_{0}}}{8}\]

C) \[\frac{{{I}_{0}}}{16}\]

D)        \[\frac{{{I}_{0}}}{2}\]

Correct Answer: B

Solution :

According to malus law, \[I={{I}_{0}}{{\cos }^{2}}\theta \] \[{{I}_{1}}=\frac{{{I}_{0}}}{2}\] \[{{I}_{2}}=\frac{{{I}_{0}}}{2}{{\cos }^{2}}45{}^\circ =\frac{{{I}_{0}}}{2}\times \frac{1}{2}=\frac{{{I}_{0}}}{4}\] \[{{I}_{3}}=\frac{{{I}_{0}}}{4}{{\cos }^{2}}45{}^\circ \Rightarrow {{I}_{3}}=\frac{{{I}_{0}}}{8}\]