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 the dimensions of $B$ are same as that of

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

Answer 1

Answer: (C)

We know that energy equation relating physical quantity should be in dimensional balance.
Hence, dimensions of terms on both sides of given equation must be same.
Given, $\mu =A+\frac{B}{{\lambda }^2}$
where refractive index is a dimensionless quantity,
hence $\frac{B}{{\lambda }^2}$ is also dimensionless
$\therefore$ Dimension of $B=$ dimension of ${\lambda }^2$
$=c{m}^2$
$=$ dimensions of area