The figure shows a double slit experiment where $P$ and $Q$ are the slits. The path lengths $PX$ and $QX$ are $n\lambda$ and $(n + 2)\lambda$ respectively,where $n$ is a whole number and $\lambda$ is the wavelength. Taking the central fringe as zero,what is formed at $X$?

$A$ beam of electrons is used in a $YDSE$ experiment. The slit width is $d$. When the velocity of the electrons is increased,then

What is the effect on the interference fringes in a Young's double-slit experiment due to each of the following operations:
$(a)$ the screen is moved away from the plane of the slits;
$(b)$ the (monochromatic) source is replaced by another (monochromatic) source of shorter wavelength;
$(c)$ the separation between the two slits is increased;
$(d)$ the source slit is moved closer to the double-slit plane;
$(e)$ the width of the source slit is increased;
$(f)$ the monochromatic source is replaced by a source of white light?
(In each operation,take all parameters,other than the one specified,to remain unchanged.)

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 a Young's double slit experiment,the slit separation is $0.2 \ cm$,the distance between the screen and slit is $1 \ m$. The wavelength of the light used is $5000 \ \mathring{A}$. The distance between two consecutive dark fringes (in $mm$) is

In Young's double-slit experiment,the intensity of light at a point on the screen where the path difference is $\lambda$ is $k$ units; $\lambda$ being the wavelength of light used. The intensity at a point where the path difference is $\lambda/4$ will be: