| In Young's double-slit experiment, the separation between two slits is \[d=0.32\text{ }mm\]and the wavelength of light used is\[\lambda =5000\text{ }\overset{o}{\mathop{A}}\,\]. Find the number of maxima in the angular range\[-{{\sin }^{-1}}(0.6)\le \theta \le {{\sin }^{-1}}(0.6)\]. |
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A) \[385\]
B) \[384\]
C) \[768\]
D) \[769\]
Correct Answer: D
Solution :
[d] Position of nth order maxima is given by \[d\sin \theta =n\lambda ;\] \[n=0,\] \[\pm 1,\pm 2,..\] At \[\sin \theta =0.6;\] \[d=0.32mm;\] \[\lambda =5000\overset{o}{\mathop{A}}\,,\] we have \[n=\frac{d\sin \theta }{\lambda }=\frac{0.32\times 0.6}{5000\times {{10}^{-7}}}=384\] It means there are 384 maxima in the range\[0<\theta <{{\sin }^{-1}}(0.6).\]. By symmetry we have the same number of maxima on the other side and there is one central maxima (corresponding to\[n=0\]). Therefore, total number of maxima \[=384+384+1\] \[=769\]
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