The ratio of resolving powers of an optical microscope for two wavelength $$\lambda $$₁ = 4000 $$\mathop A\limits^ \circ $$ and $${\lambda _2}$$ = 6000 $$\mathop A\limits^ \circ $$ is

Two polaroids P₁ and P₂ are placed with their axis perpendicular to each other. Unpolarised light $$I$$₀ is incident on P₁. A third polaroid P₃ is kept in between P₁ and P₂ such that its axis makes an angle 45^o with that of P₁. The intensity of transmitted light through P₂ is

The interference pattern is obtained with two coherent light sources of intensity ratio n. In the interference pattern, the ratio $${{{I_{max}} - {I_{\min }}} \over {{I_{max}} + {I_{min}}}}$$ will be

A linear aperture whose width is 0.02 cm is placed immediately in front of a lens of focal length 60 cm. The aparture is illuminated normally by a parallel beam of wavelength 5 $$ \times $$ 10^$$-$$5 cm. The distance of the first dark band of the diffraction pattern from the centre of the screen is