Calculate the speed of light in water if the refractive index of water is 1.33

The correct option is 2.25 x 10⁸ m/s.

To find the speed of light in water, we use the relationship between the refractive index of a medium, the speed of light in a vacuum, and the speed of light in that medium. The formula is given by:
$$n=\frac{c}{v}$$
where:
• $n$ is the refractive index of the medium (for water, $n=1.33$ or approximately $\frac{4}{3}$)
• $c$ is the speed of light in a vacuum, which is a known constant:
$$c=3\times {10}^8\text{ m/s}$$
• $v$ is the speed of light in the medium (water).

Rearranging the formula to solve for the speed of light in water ($v$):
$$v=\frac{c}{n}$$
Substitute the given values into the equation:
$$v=\frac{3\times {10}^8\text{ m/s}}{1.33}$$
Using the fraction approximation for 1.33, which is $\frac{4}{3}$:
$$v=\frac{3\times {10}^8}{\frac{4}{3}}=\frac{3\times 3\times {10}^8}{4}=\frac{9}{4}\times {10}^8$$
$$v=2.25\times {10}^8\text{ m/s}$$
Therefore, the speed of light in water is 2.25 x 10⁸ m/s.