In Young's double slit experiment, for the $n^{\text{th}}$ dark fringe ($n = 1, 2, 3, \ldots$) the phase difference of the interfering waves in radian will be

In a biprism experiment, fifth dark fringe is obtained at a point. A thin transparent film of refractive index '$\mu$' is placed in one of the interfering paths. Now $7^{th}$ bright fringe is obtained at the same point. If '$\lambda$' is the wavelength of light used, the thickness of film is equal to

A plane wavefront of width $x$, is incident on an air-water interface and the corresponding refracted wavefront has a width y as shown in figure. The refreactive index of air with respect to water in terms of distances w and z is

In an optical instrument- microscope, the wavelength of light used are $\lambda_1 = 6800$ Å and $\lambda_2 = 5100$ Å. The ratio of the resolving power of microscope corresponding to '$\lambda_1$' to that for '$\lambda_2$' is