In Young's double slit experiment, the slits are 2 mm apart and are illuminated by photons of two wavelengths $${\lambda _1}$$ = 12000 $$\mathop A\limits^ \circ $$ and $${\lambda _2}$$ = 10000 $$\mathop A\limits^ \circ $$. At what minimum distance from the common central bright fringe on the screen 2 m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other ?

The frequency of a light wave in a material is 2 $$ \times $$ 10¹⁴ Hz and wavelength is 5000 $$\mathop A\limits^ \circ $$. The refractive index of material will be

The angular resolution of a 10 cm diameter telescope at a wavelength of 5000 $$\mathop A\limits^ \circ $$ is of the order of

A telescope has an objective lens of 10 cm diameter and is situated at a distance of one kilometer from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is 5000 $$\mathop A\limits^ \circ $$, is of the order of