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

The correct option is D

Area

Step 1: Given data

The refractive index $\mu$ is given as $\mu =A+\frac{B}{{\lambda }^2}$ , where $A$ and $B$ are constants and $\lambda$ is wavelength.

Step 2: To find

The dimensions of $B$ .

Step 3: Calculation

$\mu =\frac{\mathrm{Velocity}\mathrm{of}\mathrm{the}\mathrm{light}\mathrm{in}\mathrm{vaccum}}{\mathrm{Velocity}\mathrm{of}\mathrm{the}\mathrm{light}\mathrm{in}\mathrm{medium}}$

The refractive index $\mu$ is dimension less.

$\lambda =$Wave length

The dimension of wave length is $=M^0{L}^1{T}^0$

Given equation is

$\mu =A+\frac{B}{{\lambda }^2}$

Equating the dimension we have

$$\begin{gathered} \left[\frac{B}{{\lambda }^2}\right]=M^0{L}^0{T}^0 \\ \Rightarrow \left[B\right]=\left[{\lambda }^2\right] \\ \Rightarrow \left[B\right]=M^0{L}^2{T}^0 \\ =L^2 \end{gathered}$$

The dimension of area is $=M^0{L}^2{T}^0$

Therefore, the dimension of $B$ is equal to the dimension of the area.

Hence, option D is correct.