Chapter 26.2, Problem 20PP

To determine

The speed of light in water.

Answer to Problem 20PP

The velocity of light (EM wave) through water is $\boxed{v=2.25\times {10}^8{\text{ms}}^{\text{-1}}}$ .

Explanation of Solution

Given:

The speed of light is $c=3\times {10}^8{\text{ms}}^{\text{-1}}$ .

Formula used:

The velocity of the EM wave through a dielectric medium is

  $v=\frac{c}{\sqrt{K}}$  ...... (1)

Here, $K$ is dielectric constant.

Calculation:

For water, dielectric constant is $K=1.77$.

Substitute $c=3\times {10}^8{\text{ms}}^{\text{-1}}$ for $c$ and $1.00054$ for $K$ in equation (1)

  $\begin{array}{l}v=\frac{3\times {10}^8{\text{ms}}^{\text{-1}}}{\sqrt{1.77}}\\ \boxed{v=2.25\times {10}^8{\text{ms}}^{\text{-1}}}\end{array}$

Conclusion:

Hence, the velocity of light (EM wave) through water is $\boxed{v=2.25\times {10}^8{\text{ms}}^{\text{-1}}}$ .