The path difference between two interfering light waves meeting at a point on the screen is $\left(\frac{87}{2}\right) \lambda$. The band obtained at that point is

In a Young's double slit experiment,slits are separated by $0.5 \ mm$,and the screen is placed $150 \ cm$ away. $A$ beam of light consisting of two wavelengths,$650 \ nm$ and $520 \ nm$,is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is...... $mm$.

In Young's double slit experiment,the $10^{th}$ order maximum is obtained at a point of observation in the interference pattern for a wavelength $\lambda_1 = 7000 \; \mathring{A}$. If the source is replaced by another one of wavelength $\lambda_2 = 5000 \; \mathring{A}$,what will be the order of the maximum at the same point (in $^{th}$)?

Assertion: In Young's experiment,the fringe width for dark fringes is different from that for bright fringes.
Reason: In Young's double slit experiment,if the fringes are performed with a source of white light,then only black and bright fringes are observed.

This question has Statement-$1$ and Statement-$2$. Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement-$1$: In Young's double slit experiment,the number of fringes observed in the field of view is small with longer wavelength of light and is large with shorter wavelength of light.
Statement-$2$: In the double slit experiment,the fringe width depends directly on the wavelength of light.

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: