Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the beams is $$\pi / 2$$ at point $$\mathrm{A}$$ and $$\pi$$ at point $$\mathrm{B}$$. Then the difference between the resultant intensities at $$\mathrm{A}$$ and $$\mathrm{B}$$ is

In Young's double slit experiment, the intensity at a point where path difference is $$\frac{\lambda}{6}$$ ($$\lambda$$ being the wavelength of light used) is $$I^{\prime}$$. If '$$I_0$$' denotes the maximum intensity, then $$\frac{I}{I_0}$$ is equal to $$\left(\cos 0^{\circ}=1, \cos 60^{\circ}=\frac{1}{\lambda}\right)$$

In Young's double slit experiment, the distance of $$\mathrm{n}^{\text {th }}$$ dark band from the central bright band in terms of bandwidth '$$\beta$$' is

In biprism experiment, $$6^{\text {th }}$$ bright band with wavelength '$$\lambda_1$$' coincides with $$7^{\text {th }}$$ dark band with wavelength '$$\lambda_2$$' then the ratio $$\lambda_1: \lambda_2$$ is (other setting remains the same)