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 $c{m}^2$ or area.