Question

Give an example of a physical quantity which is dimensionless.

Answer 1

Example of Dimensionless Quantity:

1. In order for a quantity to be dimensionless, it must not have any unit.
2. When the quantity is a ratio of a similar type of physical quantity, the units of the ratio cancel out.
3. Refractive index $\left(n\right)$ of a material is a quantity that is the ratio of the speed of light in vacuum $\left(c\right)$ and the speed of light in that medium $\left(v\right)$.
   $n=\frac{c}{v}$
4. Hence the unit of speed cancels out and leaves a dimensional quantity behind.
5. Therefore refractive index is an example of a dimensionless quantity.

Hence, an example of a physical quantity that is dimensionless is refractive index $\left(n\right)$.