Question

Suppose refractive index $ \mu $ is given as $ \mu =A+B/{{\lambda }^{2}}, $ where $A$ and $B$ are constants and $X$ 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.