When a thin transparent plate of thickness $t$ and refractive index $\mu$ is placed in the path of one of the two interfering waves of light,then the path difference changes by

In Young's double slit arrangement,water is filled in the space between the screen and the slits. Then:

$A$ plate of thickness $t$ made of a material of refractive index $\mu$ is placed in front of one of the slits in a double slit experiment. What should be the minimum thickness $t$ for which the intensity at the centre of the fringe pattern is zero?

$A$ flake of glass (refractive index $\mu = 1.5$) is placed over one of the openings of a double slit apparatus. The interference pattern displaces itself through seven successive maxima towards the side where the flake is placed. If the wavelength of the light used is $\lambda = 600 \, nm$,then the thickness of the flake is ........ $nm$.

In $YDSE$,the source $S$ placed symmetrically with respect to the slits $S_1$ and $S_2$ is now moved parallel to the plane of the slits so that it is closer to the upper slit $S_1$,as shown. Then,

$A$ transparent medium of refractive index $\mu = 1.5$ and thickness $t = 2.5 \times 10^{-5} \, m$ is placed in front of one of the slits in a Young's double-slit experiment. By what distance (in $cm$) will the interference pattern shift? The distance between the two slits is $d = 0.5 \, mm$ and the distance between the screen and the slits is $D = 100 \, cm$.