Question

The refractive index of a material is given by the equation $n=\frac{A+B}{{\lambda }^2}$, where $A$ and $B$ are for $B$ is

• A. $\left[M^0{L}^2{T}^{-1}\right]$
• B. $\left[M^0{L}^{-2}{T}^0\right]$
• C. $\left[M^0{L}^2{T}^{-2}\right]$
• D. $\left[M^0{L}^2{T}^0\right]$

Answer 1

Answer: (D)

Every equation relating physical quantities should be in dimensional balance. The given equation is
$n=\frac{A+B}{{\lambda }^2}$
where A and B are constants.
The dimensions of all the terms on both sides should be same
i.e., $[B]=[A]=\left[n{\lambda }^2\right]$
$\therefore [B]=\left[M^0{L}^0{T}^0\right]\left[L^2\right]$
$=\left[M^0{L}^2{T}^0\right]$