Two beams, $A$ and $B$, of plane polarized light with mutually perpendicular planes of polarization are seen 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 of the two beams are $I_A$ and $I_B$ respectively, then $\large\frac{I_A}{I_B}$ equals :
