Young's double-slit experiment is performed using microwaves of wavelength $\lambda = 3 \, cm$. The distance between the plane of the slits and the screen is $D = 100 \, cm$,and the distance between the slits is $d = 5 \, cm$. Find $(a)$ the number of maxima and $(b)$ their positions on the screen.

Two slits are separated by $0.3\, mm$. $A$ beam of $500\, nm$ light strikes the slits producing an interference pattern. Find the number of maxima observed in the angular range $-30^{\circ} < \theta < 30^{\circ}$.

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 :

If yellow light emitted by a sodium lamp in Young's double-slit experiment is replaced by monochromatic blue light of the same intensity,then:

State two conditions for obtaining sustained interference of light. In Young's double-slit experiment,using light of wavelength $400 \, nm$,interference fringes of width $'X'$ are obtained. If the wavelength of light is increased to $600 \, nm$ and the separation between the slits is halved,find the ratio of the distances between the screen and the slits in the two arrangements if the fringe width remains the same.

In a Young's double slit experiment,$I_0$ is the intensity at the central maximum and $\beta$ is the fringe width. The intensity at a point $P$ at a distance $x$ from the central maximum will be