n = c/v so v = c/n. Water has n = 4/3. Speed = 3×10⁸ ÷ 4/3 = 2.25×10⁸ m/s.

What is the Speed of Light in Water? — Refractive Index

Question

The refractive index of water is 4/3. What is the speed of light in water?

(Take speed of light in vacuum, $c = 3 \times 10^8$ m/s)

Solution — Step by Step

Recall the definition of refractive index

Refractive index $n$ is defined as the ratio of speed of light in vacuum to speed of light in the medium:

$n = \frac{c}{v}$

This is the definition — not a formula to memorise blindly. It tells us that denser the medium, slower light travels.

Rearrange for v

We want $v$ , so flip the formula:

$v = \frac{c}{n}$

Whenever $n > 1$ (which is true for all real media), light slows down. Water has $n = \frac{4}{3} \approx 1.33$ , so it slows light down to about 75% of $c$ .

Substitute values

$v = \frac{3 \times 10^8}{\frac{4}{3}}$

Dividing by a fraction means multiplying by its reciprocal:

$v = 3 \times 10^8 \times \frac{3}{4} = \frac{9 \times 10^8}{4}$

Calculate the final answer

$v = 2.25 \times 10^8 \text{ m/s}$

Speed of light in water = $2.25 \times 10^8$ m/s

Why This Works

When light enters a denser medium, it interacts with the atoms of that medium — it gets absorbed and re-emitted, absorbed and re-emitted, constantly. This chain of interactions slows the net propagation speed. The refractive index $n$ is simply a number that captures how much slower.

The formula $n = c/v$ is the quantitative statement of this: the higher the refractive index, the more the medium slows light down. Glass has $n \approx 1.5$ , diamond has $n \approx 2.4$ — light moves at barely 40% of $c$ in diamond, which is part of why it sparkles so brilliantly.

This concept is worth knowing cold for CBSE Class 10 — it directly connects to refraction, Snell's law, and the apparent depth formula, all of which are high-weightage topics in Chapter 10.

Alternative Method

We can also use the relation between refractive index and wavelength/frequency directly, but for numerical problems, the ratio method is cleanest.

Some questions give you $n$ for two different media and ask you to compare speeds. Use the same logic:

$\frac{v_1}{v_2} = \frac{n_2}{n_1}$

So if water ( $n = 4/3$ ) and glass ( $n = 3/2$ ) are compared, light travels faster in water because $n$ is smaller there.

💡 Expert Tip

Quick check: if $n > 1$ , speed in medium $<$ speed in vacuum. Always. If your answer gives $v > c$ , you've made an arithmetic error — go back and check.

Common Mistake

⚠️ Common Mistake

Students often flip the formula and compute $v = n \times c$ , getting $v = \frac{4}{3} \times 3 \times 10^8 = 4 \times 10^8$ m/s. That answer is faster than light in vacuum — physically impossible. Remember: $n = c/v$ means $v = c/n$ , not $v = cn$ . The medium always slows light down, never speeds it up.

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

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