Question

If the speed of light in air is $3\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ and the speed of light in water is reduced by a factor of $1.3$ when compared with that of the speed of light in air. Find out the speed of light in water?

Answer 1

Step 1. Given data:

Speed of light in air $\left(c\right)$ = $3\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Refractive index$\left(n\right)$ = $1.3$

Let $v$ = Speed of light in any other medium.

Step 2. Formula used:

Refractive index $\left(n\right)$ = Speed of light in air$\left(c\right)$ $/\left(v\right)$ Speed of light in water.

So, Speed of light in water $\left(v\right)$ = Speed of light in air$\left(c\right)/$Refractive index $\left(n\right)$

Step 3. Calculation:

Hence, the speed of light in water=$\frac{3\times {10}^8}{1.3}=2.87\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Thus, the speed of light in water will be $2.87\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$