QUESTION

# What will be the unit of refractive index ?A. m/sB. No unitC. kg/${m^3}$D. N

Hint: Let us write the formula for refractive index of any medium because from that we can calculate the unit of refractive index.

As we know that the refractive index of any medium is defined as the ratio of free space velocity of light (c) to the velocity of light in that medium.

As we know that velocity is the ratio of displacement and time of any object (like light etc).

And the unit of displacement is metre (m)

And the unit of time is seconds (s).

Now refractive index of medium = $\dfrac{{{\text{Free space velocity of light}}}}{{{\text{Velocity of light in that medium}}}} = \dfrac{{\dfrac{{{\text{metre}}}}{{{\text{second}}}}}}{{\dfrac{{{\text{metre}}}}{{{\text{second}}}}}} = \dfrac{{{\text{metre}}}}{{{\text{second}}}} \times \dfrac{{{\text{metre}}}}{{{\text{second}}}} = {\text{No unit}}$

So, the refractive index of a medium is unit less.

Hence, the correct option will be B.

Note: Whenever we come up with this type of problem where we are asked to find the unit of any quantity. Then we first write the formula to calculate that quantity and then in place of values we put the unit of every quantity. After solving that we will get the required unit asked for that quantity (here refractive index).