The fringe width for red colour as compared to that for violet colour is approximately (in $times$)

In Young's double-slit experiment,a thin mica sheet of thickness $12 \times 10^{-7} \ m$ is placed in the path of one of the interfering beams. It is observed that the central bright fringe shifts by a distance equal to the fringe width. If the wavelength of light used is $6 \times 10^{-7} \ m$,find the refractive index of the mica sheet.

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:

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A)$: If Young's double slit experiment is performed in an optically denser medium than air,then the consecutive fringes come closer.
Reason $(R)$: The speed of light reduces in an optically denser medium than air while its frequency does not change.
In the light of the above statements,choose the most appropriate answer from the options given below:

In Young's double slit experiment,the wavelength of red light is $7800\,\mathring{A}$ and that of blue light is $5200\,\mathring{A}$. The value of $n$ for which the $n^{th}$ bright band due to red light coincides with the $(n + 1)^{th}$ bright band due to blue light is:

In Young's double slit experiment,carried out with light of wavelength $5000 \ \mathring{A}$,the distance between the slits is $0.3 \ \text{mm}$ and the screen is at $200 \ \text{cm}$ from the slits. The central maximum is at $x=0 \ \text{cm}$. The value of $x$ for the third maxima is ............. $\text{mm}$.