A system of three polarizers P₁, P₂, P₃ is set up such that the pass axis of P₃ is crossed with respect to that of P₁. The pass axis of P₂ is inclined at 60^o to the pass axis of P₃. When a beam of unpolarized light of intensity I0 is incident on P₁, the intensity of light transmitted by the three polarizers is I. The ratio ($${{{I_0}} \over I}$$) equals (nearly) :

The value of numerical aperature of the objective lens of a microscope is 1.25. If light of wavelength 5000 $$\mathop A\limits^o $$ is used, the minimum separation between two points, to be seen as distinct, will be :

In a double slit experiment, when a thin film of thickness t having refractive index $$\mu $$. is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of t is ($$\lambda $$ is the wavelength of the light used) :

In a Young's double slit experiment, the ratio of the slit's width is 4 : 1. The ratio of the intensity of maxima to minima, close to the central fringe on the screen, will be :