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 $\lambda^{2}$
$= cm ^{2}$
$=$ dimensions of area