$A$ beam of light consisting of two wavelengths $6300 \, \mathring{A}$ and $\lambda \, \mathring{A}$ is used to obtain interference fringes in a Young's double-slit experiment. If the $4^{th}$ bright fringe of $6300 \, \mathring{A}$ coincides with the $5^{th}$ dark fringe of $\lambda \, \mathring{A}$,the value of $\lambda$ (in $\mathring{A}$) is:

Two sources of light of wavelengths $2500 \text{ Å}$ and $3500 \text{ Å}$ are used in Young's double slit experiment simultaneously. Which orders of fringes of the two wavelength patterns coincide?

In a Young's double slit experiment,if there is no initial phase difference between the light from the two slits,what is the path difference at a point on the screen corresponding to the fifth minimum?

In a Young's double-slit experiment,sources of equal intensities are used. The distance between the slits is $d$ and the wavelength of light used is $\lambda$ (where $\lambda \ll d$). Find the angular separation of the nearest points on either side of the central maximum where the intensity becomes half of the maximum value.

$A$ double slit of separation $1.5\, mm$ is illuminated by white light (between $4500\, \mathring{A} - 7000\, \mathring{A}$). On a screen $120\, cm$ away,a coloured interference pattern is formed. If a pinhole is made on this screen at a distance $3.0\, mm$ from the central white fringe,which of the following wavelengths will be absent in the transmitted light? (in $\mathring{A}$)

When monochromatic light of wavelength $600 nm$ is used in Young's double slit experiment,the fifth order bright fringe is formed at $6 mm$ from the central bright fringe on the screen. If the experiment is conducted with light of wavelength $400 nm$,the third order bright fringe will be located at: (in $mm$)