In Young's double-slit experiment,the intensity at a point on the screen where the path difference is $\lambda/6$ is $I$. If the intensity of the central bright fringe is $I_0$,then $I/I_0$ is:

$A$ beam of light consisting of two wavelengths $7000 \; \mathring{A}$ and $5500 \; \mathring{A}$ is used to obtain an interference pattern in Young's double-slit experiment. The distance between the slits is $2.5 \; mm$ and the distance between the plane of the slits and the screen is $150 \; cm$. The least distance from the central fringe,where the bright fringes due to both the wavelengths coincide,is $n \times 10^{-5} \; m$. The value of $n$ is .............

In two separate set-ups of the Young's double slit experiment,fringes of equal width are observed when lights of wavelengths in the ratio $1:2$ are used. If the ratio of the slit separation in the two cases is $2:1$,the ratio of the distances between the plane of the slits and the screen in the two set-ups is

$A$ laser light of wavelength $630 \, nm$ is incident on a pair of slits,and the fringe width of the interference pattern produced is $8.1 \, mm$. In another interference pattern produced by a different light,the fringe width is $7.2 \, mm$. Find the wavelength of this second light in $nm$.

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.)

Two slits are made $1\, mm$ apart and the screen is placed $1\, m$ away. The fringe separation when monochromatic light of wavelength $500\, nm$ is used is