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  4. In Young's double-slit experiment, d=0.1mm , D=20cm , and λ =5460 Å , the angular position of first dark fringe will be

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Q. In Young's double-slit experiment, $d=0.1mm$ , $D=20cm$ , and $\lambda =5460 \, Å$ , the angular position of first dark fringe will be

NTA AbhyasNTA Abhyas 2022

Solution:

Position of dark fringe $y=\left(2 n - 1\right)\frac{\lambda }{2}\times \frac{D}{d}=\frac{\lambda }{2}\times \frac{D}{d}$
$\therefore $ Also $\theta =\frac{y}{D}$
$=\frac{\lambda }{2 d}=2730\times 10^{- 6}\times \frac{180}{\pi }=0.16^{o}$