In $Y.D.S.E.$ using red and blue lights of wavelengths $7800 \, \mathring{A}$ and $5200 \, \mathring{A}$,the $n^{th}$ red fringe coincides with the $(n + 1)^{th}$ blue fringe. The value of $n$ is:

$A$ student is asked to measure the wavelength of monochromatic light. He sets up the apparatus as shown in the figure. $S_1, S_2, S_3$ are narrow parallel slits,$L$ is a sodium lamp,and $M$ is a microscope eyepiece. The student fails to observe interference fringes. Your first advice to him will be:

In Young's double-slit experiment using monochromatic light,the shape of the interference pattern on the screen is .....

In a Young's double-slit experiment, the distance between two coherent sources is $0.90 \, mm$ and the distance from the sources to the screen is $1 \, m$. If the distance of the second bright fringe from the center of the central bright fringe is $1 \, mm$, find the wavelength of the light used.

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?

In Young's double slit experiment,the distance between slits and the screen is $1.0\,m$ and monochromatic light of $600\,nm$ is being used. $A$ person standing near the slits is looking at the fringe pattern. When the separation between the slits is varied,the interference pattern disappears for a particular distance $d_0$ between the slits. If the angular resolution of the eye is $\frac{1}{60}^o,$ the value of $d_0$ is close to......$mm$