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., $[B] =[A]=\left[n \lambda^{2}\right]$
$\therefore [B] =\left[M^{0} L^{0} T^{0}\right]\left[L^{2}\right]$
$=\left[M^{0} L^{2} T^{0}\right]$