Question

The dimensional formula of propagation vector $\left(K\right)$ is

• A. $\left[M^{0}L{T}^{-1}\right]$
• B. $\left[M^0{L}^{-1}{T}^0\right]$
• C. $\left[M^1{L}^{-1}{T}^0\right]$
• D. $\left[M^{-1}{L}^{-1}{T}^0\right]$

Answer 1

The correct option is B

$\left[M^0{L}^{-1}{T}^0\right]$

Propagation vector

We know that the formula of the propagation vector,

$K=\frac{2\pi }{\lambda }$

where, $k=$propagation vector, and$\lambda$, wavelength.

Therefore the dimensional,

$$\begin{gathered} K=\frac{1}{\left[L^1\right]} \\ K=\left[L^{-1}\right] \\ k=\left[M^0{L}^{-1}{T}^0\right] \end{gathered}$$

Therefore the dimensional of the propagation vector, is$\left[M^0{L}^{-1}{T}^0\right]$.

Hence, the correct option is (B).