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 Young's double slit interference experiment,the slit separation is made $3$ folds. The fringe width becomes ......... times.

Two sources of light are $0.6 \, mm$ apart and the screen is placed at a distance of $1.2 \, m$ from them. $A$ light of wavelength $6000 \, \mathring{A}$ is used. The phase difference between the two light waves interfering on the screen at a point at a distance of $3 \, mm$ from the central bright band is:

In Young's double slit experiment,the slits are $2\, mm$ apart and are illuminated by light of two wavelengths $\lambda_1 = 12000\, \mathring{A}$ and $\lambda_2 = 10000\, \mathring{A}$. At what minimum distance from the common central bright fringe on the screen $2\, m$ from the slits will a bright fringe from one interference pattern coincide with a bright fringe from the other? (in $mm$)

In Young's double-slit experiment,one of the slits is painted such that its intensity is half that of the other slit. Then:

In an interference pattern,the $(n + 4)^{th}$ order blue bright fringe and the $n^{th}$ order red bright fringe coincide at a point. If the wavelengths of red and blue light are $7800 \, \mathring{A}$ and $5200 \, \mathring{A}$ respectively,then the value of $n$ is . . . . . .