question_answer

Two Polaroids \[{{P}_{1}}\]and\[{{P}_{2}}\]are placed with their axis perpendicular to each other. Un polarised light \[{{l}_{0}}\]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\[{{45}^{o}}\]with that of\[{{P}_{1}}.\]The intensity of transmitted light through\[{{P}_{2}}\] is                                                                                       

A) \[\frac{{{l}_{0}}}{16}\]                                   

B)  \[\frac{{{l}_{0}}}{2}\]

C)  \[\frac{{{l}_{0}}}{4}\]                                    

D)  \[\frac{{{l}_{0}}}{8}\]

Correct Answer: D

Solution :

                                \[{{l}_{2}}=\frac{{{l}_{0}}}{2}{{\cos }^{2}}{{45}^{o}}\] \[=\frac{{{l}_{0}}}{2}\times \frac{1}{2}\] \[=\frac{{{l}_{0}}}{4}\] \[{{l}_{3}}=\frac{{{l}_{0}}}{4}{{\cos }^{2}}{{45}^{o}}\] \[{{l}_{3}}=\frac{{{l}_{0}}}{8}\]