91Ó°ÊÓ

Interference from a pair of slits.

The path difference of two rays creating abright fringe of order$\mathit{m}$for slit separationlocalid="1663156893374" $\mathit{d}$ ,screen distance$\mathit{D}$ and wavelength localid="1663156010374" $\mathit{λ}$is

localid="1663156168036" $\mathbf{∆}\mathit{L}\mathbf{=}\mathit{m}\mathit{λ}$

path difference of two rays creating a dark fringe of order $\mathit{m}$ for slit separationlocalid="1663156062331" $\mathit{D}$ ,screen distance and wavelength $\mathit{λ}$is

$\mathbf{∆}\mathit{L}\mathbf{=}\left(m+\frac{1}{2}\right)\mathit{λ}$ .....(2)

From equation (1), path difference for the second order bright fringe is $2\mathrm{λ}$and from equation (2) the path difference for the second order dark fringe is role="math" localid="1663156500745" $\left(2+\frac{1}{2}\right)\mathrm{λ}=2.5\mathrm{λ}$.

Thus, the point for which the path difference is $2.2\mathrm{λ}$ is an intermediate state closer to the second order maxima.

From equation (2) the path difference for the third order dark fringe is,

$\left(3+\frac{1}{2}\right)\mathrm{λ}=3.5\mathrm{λ}$

Thus, the point for which the path difference is $3.5\mathrm{λ}$ is the third order minima.

From equation (1), path difference for the second order bright fringe$2\mathrm{λ}$ is and from equation (2) the path difference for the first order dark fringe is,

$\left(1+\frac{1}{2}\right)\mathrm{λ}=1.5\mathrm{λ}$

Thus, the point for which the path difference is $1.8\mathrm{λ}$ is an intermediate state closer to the second order maxima.

From equation (1) the path difference for the first order bright fringe is$1\mathrm{λ}$ .

Thus, the point for which the path difference is $1.0\mathrm{λ}$ is the first order maxima.