Question

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

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

Answer 1

Answer: (D)

$\mu =\frac{velocityoflightinvacuum}{velocityoflightinmedium}$
The refractive index $\mu$ is dimensionless, so each term on right hand side is dimensionless. Hence, $\frac{B}{{\lambda }^2}$ is dimensionless.
This implies that dimensions of B will have the dimensions of
${\lambda }^2$ ie, of area. ie, of $c{m}^2$ or area.