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^o makes the two beams appear equally bright. If the initial intensities of the two beams are I_A and I_B respectively, then $\frac{{\text{I}}_{\text{A}}}{{\text{I}}_{\text{B}}}$ equals :