Two beams, A and B, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when…

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 $\displaystyle 30$° makes the two beams appear equally bright. If the initial intensities of the two beams are $\displaystyle \mathrm{I}_{\mathrm{A}}$ and $\displaystyle \mathrm{I}_{\mathrm{B}}$ respectively, then $\displaystyle \frac{\mathrm{I}_{\mathrm{A}}}{\mathrm{I}_{\mathrm{B}}}$ equals :