Two coherent sources of light $S_1$ and $S_2,$ equidistant from the origin, are separated by a distance $2\mathrm{\lambda }$ as shown. They emit light of wavelength $\lambda$. Interference is observed on a screen placed along the circle of a large radius $R$. Point is seen to be a point of constructive interference. Then angle $\mathrm{\theta }$ (other than $0°$ and $90°$) is 

In the figure shown, a parallel beam of light is incident on the plane of the slits of Young’s double-slit experiment. Light incident on the slit, $S_1$ passes through a medium of variable refractive index $\mathrm{\mu }=1+ax$ (where $‘\mathrm{x}’$ is the distance from the plane of slits as shown), up to a distance $‘l’$ before falling on $S_1$. Rest of the space is filled with air. If at $‘O’$ a minima is formed, then the minimum value of the positive constant $a$ (in terms of $l$ and wavelength $‘\mathrm{\lambda }’$ in air) is :

$M_1$ and$M_2$ are two plane mirrors that are kept parallel to each other as shown. There is a point $\text{'}O\text{'}$ on a perpendicular screen just in front of $\text{'}S\text{'}$. What should be the wavelength of light coming from monochromatic source $\text{'}S\text{'}$, so that a maxima is formed at $\text{'}O\text{'}$ due to interference of reflected light from both the mirrors. [Consider only $1^{st}$, reflection].$[D>>d, d>>\mathrm{\lambda }]$

A long narrow horizontal slit lies $1 \mathrm{mm}$, above a plane mirror. The interference pattern produced by the slit and its image is viewed on a screen $\sum _{}$distant $1 \mathrm{m}$, from the slit. The wavelength of light is $600 \mathrm{nm}$. Then the distance of the first maxima above the mirror is equal to $(d<<D):$

In the figure shown three slits $s_1, s_2$ and $s_3$ are illuminated with light of wavelength $\mathrm{\lambda }. \left( \mathrm{\lambda }<<d \right)$ and $D\mathit{>}>d.$ Each slit produces the same intensity $I$ on the screen. If resultant intensity at the point on the screen directly in front of $s_2$ is $3I$, then the maximum value of $\mathrm{\lambda }$ is $\frac{n{d}^2}{2D}$$\left(\mathrm{i}\right)$ Find the value of $n$, $\left(\mathrm{ii}\right)$ Also find intensity at a point $P$ if $\mathrm{\lambda }$ is of part $\left(\mathrm{i}\right)$.

A narrow monochromatic beam of light of intensity $I$ is incident on a glass plate as shown in the figure. Another identical glass plate is kept close to the first one and parallel to it. Each glass plate reflects $25 \%$ of the light incident on it and transmits the remaining. The ratio of the minimum and the maximum intensities in the interference pattern formed by the two beams obtained after one reflection at each plate is $1:n$, find value of $n.$ 

In a Young's experiment, the upper slit is covered by a thin glass plate of the refractive index $1.4$ while the lower slit is covered by another glass plate having the same thickness as the first one but having refractive index $1.7.$ Interference pattern is observed using light of wavelength $5400 \mathrm{\AA }.$ It is found that the point$P$ on the screen where the central maximum fell before the glass plates were inserted now has $(\frac{3}{4}{)}^{\mathrm{th}}$ the original intensity. It is further observed that what used to be the $5^{\mathrm{th}}$ maximum earlier, lies below the point $O$ while the $6^{\mathrm{th}}$ minimum lies above $O.$ The thickness of the glass plate is $n\times {10}^{–7}\mathrm{m}$. Find the value of $n.$ (Absorption of light by glass plate may be neglected)