A parallel beam of light of wavelength $$\lambda $$ is incident normally on a narrow slit. A diffraction pattern formed on a screen placed perpenficular to the direction of the incident beam. At the second minimum of the diffraction pattern, the phase difference between the rays coming from the two edges of slit is

In Young's double slit experiment the distance between the slits and the screen is doubled. The separation between the slits is reduced to half. As a result the fringe width

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