A) \[\lambda ={{b}^{2}}/d\]
B) \[\lambda =2\,\,{{b}^{2}}/d\]
C) \[\lambda =3\,\,{{b}^{2}}/d\]
D) \[\lambda =2\,\,{{b}^{2}}/3d\]
Correct Answer: A
Solution :
Positions of minima are given by \[{{y}_{n}}=\left( n-\frac{1}{2} \right)\,\,\frac{D\,\lambda }{d}\] \[\lambda \,\,=\,\,\frac{2\,\,{{y}_{n}}\,d}{(2\,n\,-1)\,D}\] Here, \[{{\operatorname{y}}_{n}}\,\,=\,\,b/2,\,\,d=b,\,\,D=d\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\lambda =\frac{{{b}^{2}}}{(2n-1)d}\] where \[\operatorname{n}\,\,=\,\,1, 2,\,\,3,....\] Hence, \[\lambda =\frac{{{b}^{2}}}{d},\,\,\,\frac{{{b}^{2}}}{3\,d},\,\,....\]You need to login to perform this action.
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