In Young's double-slit experiment,when light of wavelength $\lambda_1 = 5898 \ \mathring{A}$ is used,$92$ fringes are observed in a certain region. If light of wavelength $\lambda_2 = 5461 \ \mathring{A}$ is used instead,how many fringes will be observed in the same region?

For Young's double slit experiment,two statements are given below :
Statement $I:$ If the screen is moved away from the plane of the slits,the angular separation of the fringes remains constant.
Statement $II:$ If the monochromatic source is replaced by another monochromatic source of larger wavelength,the angular separation of the fringes decreases.
In the light of the above statements,choose the correct answer from the options given below :

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.

In Young's double slit experiment,the two slits act as coherent sources of equal amplitude $A$ and wavelength $\lambda$. In another experiment with the same setup,the two slits are sources of equal amplitude $A$ and wavelength $\lambda$ but are incoherent. The ratio of the intensity of light at the midpoint of the screen in the first case to that in the second case is:

In a Young's double-slit experiment,$12$ fringes are observed to be formed in a certain segment of the screen when light of wavelength $600 \ nm$ is used. If the wavelength of light is changed to $400 \ nm$,the number of fringes observed in the same segment of the screen is:

In a Young's double-slit experiment,the distance between the two slits is twice the wavelength of the light used. Find the total number of bright fringes formed on the screen.