Monochromatic green light of wavelength $5 \times 10^{-7} \, m$ illuminates a pair of slits $1 \, mm$ apart. The separation of bright lines (fringe width) on the interference pattern formed on a screen $2 \, m$ away is ...... $mm$.

The path difference between two interfering light waves meeting at a point on the screen is $\left(\frac{57}{2}\right) \lambda$. The band obtained at that point is

Consider the following statements in the case of Young's double-slit experiment:
$(1)$ $A$ slit is necessary if we use an ordinary extended source of light.
$(2)$ $A$ slit is not necessary if we use an ordinary but well-collimated beam of light.
$(3)$ $A$ slit is not needed if we use a spatially coherent point source of light.
Which of the above statements is true?

In Young's double-slit experiment,monochromatic light is used to illuminate the two slits $A$ and $B$. Interference fringes are observed on a screen placed in front of the slits. If a thin glass plate is placed normally in the path of the beam coming from slit $A$,then:

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

Two slits separated by a distance of $1 \,mm$ are illuminated with light of wavelength $6.5 \times 10^{-7} \,m$. The interference fringes are observed on a screen placed at $1 \,m$ from the slits. The distance between the third dark fringe and the fifth bright fringe is equal to (in $\,mm$)