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Question

Give an example of a physical quantity which is dimensionless.


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Solution

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 n of a material is a quantity that is the ratio of the speed of light in vacuum c and the speed of light in that medium v.
    n=cv
  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 n.


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