Question

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

• A. Wavelength
• B. Volume
• C. Pressure
• D. Area

Answer 1

The correct option is D Area

We know that refractive index is the ratio of speed of light (same quantity) in two different mediums.
Thus, refractive index is dimensionless.

$\left[\mu \right]=$ dimensionless

By principle of homogeneity,

$\left[A\right]=$ dimensionless, and

$\left[\frac{B}{{\lambda }^2}\right]=$ dimensionless

$\Rightarrow \left[B\right]=\left[{\lambda }^2\right]$

$\Rightarrow \left[B\right]=\left[L^2\right]$

$\Rightarrow \left[B\right]=\left[\text{Area}\right]$

So, option $\left(d\right)$ is correct.