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In Young's double slit experiment the two slits are d distance apart. Interference pattern is observed on a screen at a distance D from the slits. A dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light is
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Verified Answer
The correct answer is:
\(\frac{\mathrm{d}^2}{\mathrm{D}}\)
Hints: 
\(\mathrm{n}^{\text {th }}\) Dark fringe
\(\begin{aligned}
& (2 n-1) \frac{D \lambda}{2 d}=\frac{d}{2} \\
& \lambda=\frac{d^2}{(2 n-1) D}=\frac{d^2}{D} \quad[\text { for } n=1]
\end{aligned}\)
\(\mathrm{n}^{\text {th }}\) Dark fringe
\(\begin{aligned}
& (2 n-1) \frac{D \lambda}{2 d}=\frac{d}{2} \\
& \lambda=\frac{d^2}{(2 n-1) D}=\frac{d^2}{D} \quad[\text { for } n=1]
\end{aligned}\)
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