First slide

Dimensions of physical quantities

Question

$μ = A + \frac{B}{λ} + \frac{C}{λ^{2}}$ is dimensionally correct the dimensions of $A, B & C$ respectively are $(μ, A, B, C$ are constants where $λ$ is wave length and $μ$ is refractive index)

Moderate

A

No Dimensions, $L, L^{2}$
B

$L^{2},$ No Dimensions, $L$
C

$L, L^{2},$ No Dimensions
D

$L,$ No dimensions, $L^{2}$

Solution

$\begin{array}{l} g i v e n μ = A + \frac{B}{λ} + \frac{C}{λ^{2}} \\ R e f r a c t i v e i n d e x μ = \frac{\sin i}{\sin r} = M^{0} L^{0} T^{0}; \\ λ i s w a v e l e n g t h = L \\ A c c o r d i n g t o p r i n c i p l e o f h o m o g e n e i t y \\ d i m e n s i o n s o f A = μ = n o d i m e n s i o n s \\ \frac{B}{λ} = μ \\ \Rightarrow B = μ λ \\ \Rightarrow B = L \\ \frac{C}{λ^{2}} = μ \\ \Rightarrow C = μ λ^{2} \\ \Rightarrow C = L^{2} \end{array}$

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