Question

Two beams $A$ and $B$ of plane polarized light with mutually perpendicular planes of polarization are through a polaroid. From the position when the beam $A$ has maximum intensity (and beam $B$ has zero intensity), a rotation of polaroid through ${30}^{\circ }$ makes the two beams appear equally bright. If the initial intensities is of the two beams are $I_A$ and $I_B$ respectively, then $\frac{I_A}{I_B}$ is equal to,

• A. $3$
• B. $\frac{1}{3}$
• C. $1$
• D. $\frac{3}{2}$

Answer 1

The correct option is B $\frac{1}{3}$

According to Malu's law,
$I=I_0{\cos }^2\theta$

For first arrangement, the beam $A$ has maximum intensity and beam $B$ has zero intensity. So, ${\theta }_{\left(A1\right)}=0^{\circ },{\theta }_{\left(B1\right)}={90}^{\circ }$

After ${30}^{\circ }$ rotation, ${\theta }_{\left(A2\right)}={30}^{\circ },{\theta }_{\left(B2\right)}={60}^{\circ }$

$\Rightarrow I_1=I_A{\cos }^2{30}^{\circ }$

and $I_2=I_B{\cos }^2{60}^{\circ }$

Since, both the beams have equal intensities in second arrangement, we can write, $I_1=I_2$

$\therefore I_A{\cos }^2{30}^{\circ }=I_B{\cos }^2{60}^{\circ }\therefore \frac{I_A}{I_B}=\frac{1}{3}$

Hence, $\left(D\right)$ is the correct answer.