In two different Young's double-slit experiments,the fringe width is the same when the ratio of wavelengths is $1:2$. If the ratio of the distance between the slits in the two cases is $2:1$,then the ratio of the distance between the slits and the screen in the two experiments is:

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 $:$

Sodium light $(\lambda = 6 \times 10^{-7} \ m)$ is used to produce an interference pattern. The observed fringe width is $0.12 \ mm$. The angle between the two wave trains is:

In Young's double-slit experiment,when two light waves form the third minimum,they have:

Using monochromatic light of wavelength $\lambda$,an experimentalist sets up the Young's double slit experiment in three ways as shown. If she observes that $y = \beta'$,the wavelength of light used is.....$nm$

In a Young's double slit experiment,the angular width of a fringe formed on a distant screen is $1^{\circ}$. The wavelength of the light used is $6280 \; \mathring{A}$. The distance between the two coherent sources is $...........\,mm$.