The speed of light in a medium is given by the equation:

$$ v = \frac{c}{\sqrt{\varepsilon_r \mu_r}} $$

where:

• $c$ is the speed of light in vacuum (approximately $3 \times 10^8$ m/s),
• $\varepsilon_r$ is the relative permittivity of the medium (in this case, distilled water, and is given as 81),
• $\mu_r$ is the relative permeability of the medium (given as 1 for distilled water).

Substituting the given values into the equation, we get:

$$ v = \frac{3 \times 10^8 \, \text{m/s}}{\sqrt{81 \times 1}} $$

$$ v = \frac{3 \times 10^8 \, \text{m/s}}{9} $$

$$ v = 3.33 \times 10^7 \, \text{m/s} $$

So, the speed of light in distilled water is $3.33 \times 10^7$ m/s.