If the distance between the first maxima and the fifth minima of a double slit pattern is $7\,mm$ and the slits are separated by $0.15\,mm$ with the screen $50\,cm$ from the slits,then find the wavelength of the light used in $nm$.

In Young's double slit experiment,the $y$-coordinates of the central maxima and the $10^{th}$ maxima are $2 \, cm$ and $5 \, cm$ respectively. When the $YDSE$ apparatus is immersed in a liquid of refractive index $\mu = 1.5$,what will be the corresponding $y$-coordinates?

The distance between two coherent sources is $0.1 \, mm$. The fringe-width on a screen $1.2 \, m$ away from the source is $6.0 \, mm$. The wavelength of light used is ......... $\mathring{A}$.

Given below are two statements. One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A) :$ In Young's double slit experiment,the fringes produced by red light are closer as compared to those produced by blue light.
Reason $(R) :$ The fringe width is directly proportional to the wavelength of light.
In the light of above statements,choose the correct answer from the options given below $:$

In a $YDSE$,the central bright fringe can be identified:

Consider the following statements in the case of Young's double-slit experiment:
$(1)$ $A$ slit is necessary if we use an ordinary extended source of light.
$(2)$ $A$ slit is not necessary if we use an ordinary but well-collimated beam of light.
$(3)$ $A$ slit is not needed if we use a spatially coherent point source of light.
Which of the above statements is true?