A Youngs slits experiment is set up in which two narrow slits, of separation d, are illuminated by light of wavelength . The diffraction pattern

A Young’s slits experiment is set up in which two narrow slits, of separation d, are illuminated by light of wavelength λ. The diffraction pattern is viewed on a screen at a distance D. Derive expressions for the intensity distribution on the screen and the separation of the fringes.
If D = 1m, λ = 600nm, and the distance from the centre of the fringe pattern to the 10th bright band on one side is 30 mm, calculate the separation d of the slits.
A film of transparent material is placed over one of the slits, and the displacement of the centre of the fringe pattern is observed to be 30 mm. Calculate the refractive index of the material if its thickness is 20 μm.