Two coherent sources $P$ and $Q$ produce interference at a point $A$ on the screen where there is a dark band which is formed between $4^{\mathrm{th}}$ bright band and $5^{\mathrm{th}}$ bright band. The wavelength of light used is $6000 \stackrel{\circ }{\mathrm{A}}$. The path difference between $PA$ and $QA$ is

A beam of light of $\lambda =600 \mathrm{nm}$ from a distant source falls on a single slit $1 \mathrm{mm}$ wide and the resulting diffraction pattern is observed on a screen $2 \mathrm{m}$ away. The distance between the first dark fringes on either side of the central bright fringe is

A fringe width of a certain interference pattern is $\beta =0.002 \mathrm{cm}$. What is the distance of $5^{\mathrm{th}}$ order minima from central maxima?

Two slits separated by a distance of $1 \mathrm{mm}$ are illuminated with light of wavelength $4\times {10}^{-7} \mathrm{m}$. The interference fringes are observed on a screen placed $1 \mathrm{m}$ from the slits. The distance between the fourth dark and sixth bright fringe on the same side is equal to

In Young's double-slit experiment, the intensity at a point where the path difference is $\frac{\lambda }{6}$ ($\lambda$ being the wavelength of the light used) is $I$. If $I_0$ denotes the maximum intensity, then $\frac{I}{I_0}$ is equal to

If a transparent medium of refractive index $\mu =1.5$ and thickness $t=2.5\times {10}^{-5} \mathrm{m}$ is inserted in front of one of the slits of Young's double-slit experiment, how much will be the shift in the interference pattern? The distance between the slits is $0.5 \mathrm{mm}$ and that between slits and screen is $100 \mathrm{cm}$.

Young's double-slit experiment is first performed in air and then in a medium other than air. It is found that $8^{\mathrm{th}}$ bright fringe in the medium lies where $5^{\mathrm{th}}$ dark fringe lies in the air. The refractive index of the medium is nearly

In Young's experiment, two coherent sources are placed $0.90 \mathrm{mm}$ apart and the fringes are observed one metre away. If it produces the second dark fringe at a distance of $1 \mathrm{mm}$ from the central fringe, the wavelength of monochromatic light used would be