Question

Two beams $A$ and $B$ of plane polarised light with mutually perpendicular planes of polarisation are seen through a polaroid from the position where beam $A$ has maximum intensity. A rotation of polaroid through $60^{\circ }$ makes two beams appears equally intense. If initial intensities of two beams is $I_A$ and $I_B$ then $\frac{I_A}{I_B}$ equals

• A. $3$
• B. $\frac{3}{2}$
• C. $\frac{2}{3}$
• D. $9$

Answer 1

Answer: (A)

By Malus law
$I_A^{\prime }=I_A{\cos }^{2}60^{\circ }$
$I_B^{\prime }=I_B{\cos }^{2}30^{\circ }$
$I_A^{\prime }=I^{\prime }B\therefore I_A\times {\cos }^{2}60^{\circ }$
$=I_B{\cos }^{2}30^{\circ }$
$I_A\times \frac{1}{4}=I_B\times \frac{3}{4}$
$\frac{I_A}{I_B}=3$