A) \[[{{M}^{0}}{{L}^{2}}{{T}^{-1}}]\]
B) \[[{{M}^{0}}{{L}^{-2}}{{T}^{0}}]\]
C) \[[{{M}^{0}}{{L}^{2}}{{T}^{-2}}]\]
D) \[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\]
Correct Answer: D
Solution :
Key Idea: Every equation relating physical quantities should be in dimensional balance. The given equation is \[n=\frac{A+B}{{{\lambda }^{2}}}\] where A and B are constants. The dimensions of all the terms on both sides should be same i.e, \[[B]=[A]=[n{{\lambda }^{2}}]\] \[\therefore \] \[[B]=[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\,[{{L}^{2}}]\] \[=[{{M}^{0}}{{L}^{2}}{{T}^{0}}]\]
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