$A$ mixture of light of wavelength $590 \, nm$ and an unknown wavelength is incident on the two slits of a Young's double-slit experiment. The central bright fringes of both lights coincide. The $3^{rd}$ bright fringe of the known wavelength coincides with the $4^{th}$ bright fringe of the unknown wavelength. Find the unknown wavelength in $nm$.

In a Young's double-slit experiment,the distance between the two slits is $d = \lambda / 4$,where $\lambda$ is the wavelength of the light used. The initial phase difference is $\pi / 4$. What is the intensity at $\theta = 30^o$?

If yellow light in the Young's double slit experiment is replaced by red light,the fringe width will

In Young's double-slit interference experiment,the distance between two sources is $0.1 \ mm$. The distance of the screen from the sources is $20 \ cm$. The wavelength of light used is $5460 \ \mathring{A}$. What is the angular position of the first dark fringe in degrees?

In $Y.D.S.E.,$ the slits are $0.2 \, cm$ apart and are illuminated by yellow light $(\lambda = 600 \, nm).$ What would be the fringe width on a screen placed $1 \, m$ from the plane of the slits if the whole system is immersed in water of refractive index $\mu = \frac{4}{3}$ (in $, mm$)?

Given below are two statements:
Statement $I$: In a Young's double slit experiment, the angular separation of fringes will increase as the screen is moved away from the plane of the slits.
Statement $II$: In a Young's double slit experiment, the angular separation of fringes will increase when a monochromatic source is replaced by another monochromatic source of higher wavelength.
In the light of the above statements, choose the correct answer from the options given below: