On replacing a thin film of mica of thickness $$12 \times 10^{-5} \mathrm{~cm}$$ in the path of one of the interfering beams in Young's double slit experiment using monochromatic light, the fringe pattern shifts through a distance equal to the width of bright fringe. If $$\lambda=6 \times 10^{-5} \mathrm{~cm}$$, the refractive index of mica is

When two light waves each of amplitude '$$A$$' and having a phase difference of $$\frac{\pi}{2}$$ superimposed then the amplitude of resultant wave is

Two wavelengths of sodium light $$590 \mathrm{~nm}$$ and $$596 \mathrm{~nm}$$ are used one after another to study diffraction due to single slit of aperture $$2 \times 10^{-6} \mathrm{~m}$$. The distance between the slit and the screen is $$1.5 \mathrm{~m}$$. The separation between the positions of first maximum of the diffraction pattern obtained in the two cases is

The diffraction fringes obtained by a single slit are of