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 Young's double slit experiment,if the separation between coherent sources is halved and the distance of the screen from the coherent sources is doubled,then the fringe width becomes:

The ratio of intensities at two points on the screen in Young's double slit experiment when waves from the two slits have a path difference of $0$ and $\lambda/4$ ($\lambda$ is the wavelength of light used) $(\cos 0^\circ = 1, \cos \pi/2 = 0)$.

Two ideal slits $S_1$ and $S_2$ are at a distance $d$ apart and are illuminated by light of wavelength $\lambda$ passing through an ideal source slit $S$ placed on the line through $S_2$ as shown. The distance between the plane of the slits and the source slit is $D$. $A$ screen is held at a distance $D$ from the plane of the slits. The minimum value of $d$ for which there is darkness at $O$ is

In which of the following is the interference due to the division of wave front?

Using Young's double slit experiment,a monochromatic light of wavelength $5000 \,\mathring A$ produces fringes of fringe width $0.5 \,mm$. If another monochromatic light of wavelength $6000 \,\mathring A$ is used and the separation between the slits is doubled,then the new fringe width will be ............... $mm$.