In a double slit experiment with monochromatic light,fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by $5 \times 10^{-2} \,m$ towards the slits,the change in fringe width is $3 \times 10^{-3} \,cm$. If the distance between the slits is $1 \,mm$,then the wavelength of the light will be . . . . . . $nm$.

If the source of light used in a Young's Double Slit Experiment is changed from red to blue,then

In Young's experiment,the ratio of maximum to minimum intensities of the fringe system is $4:1$. The amplitudes of the coherent sources are in the ratio: (in $:1$)

In $Y.D.S.E.$,the separation between the two slits $S_1$ and $S_2$ is $a$,and the screen is at a distance $x$ from the slits. The light source $S$ is moving with velocity $v$ parallel to the line joining $S_1$ and $S_2$ and is at a perpendicular distance $h$ from the plane of the slits. What is the frequency of change in brightness at the central point on the screen?

In Young's double slit experiment,the $10^{th}$ order maximum is obtained at a point of observation in the interference pattern for a wavelength $\lambda_1 = 7000 \; \mathring{A}$. If the source is replaced by another one of wavelength $\lambda_2 = 5000 \; \mathring{A}$,what will be the order of the maximum at the same point (in $^{th}$)?

$A$ Young's double slit interference arrangement with slits $S_1$ and $S_2$ is immersed in water (refractive index $\mu_w = 4/3$) as shown in the figure. The positions of maxima on the surface of water are given by $x^2 = p^2 m^2 \lambda^2 - d^2$,where $\lambda$ is the wavelength of light in air (refractive index $\mu_a = 1$),$2d$ is the separation between the slits,and $m$ is an integer. The value of $p$ is