A) 450 nm
B) 400 nm
C) 500 nm
D) 600 nm
Correct Answer: D
Solution :
The distance between two consecutive dark or bright fringes is recognised as \[\beta \] (fringe width) and that between central fringe and first dark fringe on either side is \[\frac{\beta }{2}\] Given, spacing between second dark fringe and central fringe \[=\beta +\frac{\beta }{2}\] or \[\frac{3\,\beta }{2}=1\,\,mm\] or \[\beta =\frac{2}{3}\times 1\,mm\] or \[\frac{\lambda \,D}{d}=\frac{2}{3}\,mm\] \[\therefore \] \[\lambda =\frac{2}{3}\times {{10}^{-3}}\times \frac{0.9\times {{10}^{-3}}}{1}\] \[\Rightarrow \] \[\lambda =0.6\times {{10}^{-6}}m\] \[\therefore \] \[\lambda =600\times {{10}^{-9}}m\] \[=600\,\,nm\]
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