In Young's double-slit experiment,$I_0$ is the intensity of the central maximum and $\beta$ is the fringe width. The intensity at a point $P$ at a distance $x$ from the center is:

In Young's double-slit experiment,the intensity at a point on the screen is $I_0/4$. Find the angular position of this point.

In Young's double-slit experiment,the slits are separated by $0.2 \, cm$ and illuminated by light of wavelength $\lambda = 5896 \, \mathring{A}$. What is the fringe width on a screen placed $1 \, m$ away from the plane of the slits? What will be the fringe width if the entire system is immersed in water (in $, mm$)? (Refractive index of water $\mu_w = 4/3$)

In a Young's double-slit experiment,$92$ fringes are observed when sodium light $(\lambda = 5898 \, \mathring A)$ is used. If light of wavelength $\lambda = 5461 \, \mathring A$ is used instead,how many fringes will be observed?

The distance between two coherent sources is $1 \ mm$. The screen is placed at a distance of $1 \ m$ from the sources. If the distance of the third bright fringe is $1.2 \ mm$ from the central fringe, the wavelength of light used is:

$A$ 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 $\mathring{A}$)