Question

Suppose refractive index $\mu$ is given as $\mu=A+B / \lambda^{2}$, where $A$ and $B$ are constants and is wavelength then the dimensions of $B$ are same as that of:

• A. wavelength
• B. pressure
• C. area
• D. volume

Answer 1

Answer: (C)

From the relation $\mu=\frac{\text { velocity of light in vacuum }}{\text { velocity of light in medium }}$
Therefore, refractive index $\mu$ is dimensionless, so each term on right hand side is dimensionless.
Hence, $\frac{\beta}{\lambda^{2}}$ is dimensionless.
This implies that dimensions of $\beta$ will have the dimensions of
$\lambda^{2}$. i.e., of $cm ^{2}$ or area.