In Young's double-slit experiment,if a metal plate of thickness $t$ is placed in the path of one of the rays,then:

Two coherent sources $O_1$ and $O_2$ in Young's double slit experiment are illuminated with monochromatic light of wavelength $5000 \text{ Å}$. If a second order dark fringe is formed at a point $R$ on the screen,the path difference $O_1 R \sim O_2 R$ is (in $\mu m$)

In a double-slit experiment performed in air, the angular width of a fringe is found to be $0.15^{\circ}$ on a screen placed $80 \ cm$ away. The wavelength of light used is $490 \ nm$. What is the angular width of the fringe if the entire apparatus is immersed in a medium of refractive index $\frac{5}{3}$ (in $^{\circ}$)?

In Young's double-slit experiment,the two slits are $2 \, mm$ apart and are illuminated by a mixture of two wavelengths $\lambda_1 = 12000 \, \mathring{A}$ and $\lambda_2 = 10000 \, \mathring{A}$. At what minimum distance from the common central bright fringe on the screen will a bright fringe from one interference pattern coincide with a bright fringe from the other? The distance between the slits and the screen is $2 \, m$.

In an interference experiment,the third bright fringe is obtained using light of wavelength $700 \, nm$. What should be the wavelength of light to obtain the fifth bright fringe at the same point?

In Young's double-slit experiment, light of wavelength $4000 \, Å$ is used to produce bright fringes of width $0.6 \, mm$ at a distance of $2 \, m$ from the slits. If the whole apparatus is immersed in a liquid of refractive index $1.5$, what will be the new fringe width in $mm$?