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° makes the two beams appear equally bright. If the initial intensities of the two beams are \[{{\text{I}}_{\text{A}}}\] and \[{{\text{I}}_{\text{B}}}\]respectively, then \[\frac{{{\text{I}}_{\text{A}}}}{{{\text{I}}_{\text{B}}}}\]equals: [JEE MAIN 2014]