A thin convex lens made from crown glass $$\left( {\mu = {3 \over 2}} \right)$$ has focal length $$f$$. When it is measured in two different liquids having refractive indices $${4 \over 3}$$ and $${5 \over 3},$$ it has the focal lengths $${f_1}$$ and $${f_2}$$ respectively. The correct relation between the focal lengths is :

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 $${{\rm I}_A}$$ and $${{\rm I}_B}$$ respectively, then $${{{{\rm I}_A}} \over {{{\rm I}_B}}}$$ equals:

A green light is incident from the water to the air - water interface at the critical angle $$\left( \theta \right)$$. Select the correct statement.

A beam of unpolarised light of intensity $${{\rm I}_0}$$ is passed through a polaroid $$A$$ and then through another polaroid $$B$$ which is oriented so that its principal plane makes an angle of $${45^ \circ }$$ relative to that of $$A$$. The intensity of the emergent light is