JEE Main 2014 — Wave Optics Question with Solution

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 $${\mathrm{I}}_A$$ and $${\mathrm{I}}_B$$ respectively, then $$\frac{{\mathrm{I}}_A}{{\mathrm{I}}_B}$$ equals: