$A$ calcite crystal is placed over a dot on a piece of paper and rotated. On seeing through the calcite,one will see:

When a plane-polarised light is passed through an analyser and the analyser is rotated through $90^{\circ}$,the intensity of the emerging light

$A$ polarizer and an analyzer are placed such that the intensity of the transmitted light is maximum. If the analyzer is rotated by $60^{\circ}$,find the intensity of the transmitted light.

$A$ beam of natural light falls on a system of $5$ polaroids,which are arranged in succession such that the pass axis of each polaroid is turned through $60^{\circ}$ with respect to the preceding one. The fraction of the intensity of incident light that passes through the system is:

$A$ polarized light of intensity $I_{0}$ is passed through another polarizer whose pass axis makes an angle of $60^{\circ}$ with the pass axis of the former. What is the intensity of emergent polarized light from the second polarizer?

Three polaroid sheets are kept parallel to each other such that the first and the last are crossed. Unpolarised light of intensity $32 \ W m^{-2}$ falls normally on the first sheet and passes through all the polaroid sheets. If the intensity of the emerging light from the third sheet is $3 \ W m^{-2}$,then the angle between the axes of the first two polaroid sheets is: (in $^{\circ}$)