Refractive index

Drop a straw into a glass of water and it looks snapped at the surface. Push a laser through water and then through diamond at the very same angle, and the diamond bends it far more sharply. Both effects trace to one number attached to every transparent material: its refractive index. It tells you, precisely, how much slower light travels inside that material compared with vacuum — and that single ratio is what Snell's law uses to predict every bend of every ray. This article builds the definition of absolute and relative refractive index from the speed of light, connects it to Snell's law, and works through the numbers CBSE Class 10 expects you to handle confidently: water at $1.33$ , glass at $1.5$ , diamond at $2.42$ .

The core insight

Refractive index $n = c/v$ measures how much a medium slows light down relative to vacuum, and the ratio of two such speeds is exactly the constant $n_{21}$ that Snell's law uses to predict how much a ray bends at a boundary.

The core idea

Absolute refractive index. For any transparent medium, compare the speed of light in vacuum with the speed of light inside the medium:

n = \frac{c}{v}

where: $n$ is the absolute refractive index (no units), $c = 3\times10^8\ \text{m/s}$ is the speed of light in vacuum (air is close enough to use the same value), and $v$ is the speed of light inside the medium. Because light never travels faster inside a material than it does in vacuum, $v \leq c$ always, which forces $n \geq 1$ for every real medium. A bigger $n$ means a slower $v$ , and a slower $v$ means the medium is optically denser — nothing to do with its mass density.

Relative refractive index. When light crosses directly from one medium into another, the number that governs the bend is the relative refractive index of the second medium with respect to the first:

n_{21} = \frac{v_1}{v_2} = \frac{n_2}{n_1}

where: $v_1, v_2$ are the speeds of light in medium 1 and medium 2, and $n_1, n_2$ are their absolute refractive indices. This is the exact same $n_{21}$ that appears in Snell's law, $\dfrac{\sin i}{\sin r} = n_{21}$ , so refractive index is not an abstract label — it is the number you plug straight into the angle equation. The diagram below shows why: going from a rarer medium (smaller $n$ ) into a denser one (larger $n$ ) always bends the ray towards the normal, because the ray slows down as it crosses the boundary.

Figure

A ray of light crossing from a rarer medium into a denser medium, bending towards the normal line at the boundary

A quick reference set of absolute refractive indices, worth memorising for CBSE numericals: air/vacuum $\approx 1$ , water $\approx 1.33$ , glass $\approx 1.5$ , diamond $\approx 2.42$ . Diamond's very high refractive index — one of the highest among common transparent materials — is exactly why it bends and disperses light so dramatically, giving it its characteristic sparkle. It helps to keep the two directions of the rule straight in words, not just symbols. Going from a rarer medium into a denser one (say, from air into glass) always bends the ray towards the normal, and the ray also slows down as it crosses. Going the other way, from a denser medium into a rarer one (glass back into air), the ray bends away from the normal and speeds up again. This pair of rules, together with the numerical values above, is enough to answer almost every qualitative "which way does it bend" question CBSE asks about refractive index.

Derivation AGetting relative refractive index from two absolute refractive indices

Goal: starting only from the definition $n = c/v$ applied separately to two media, show algebraically why the relative refractive index of medium 2 with respect to medium 1 works out to be the simple ratio $n_{21} = n_2/n_1$ , and why this is the same quantity Snell's law calls the constant of proportionality between $\sin i$ and $\sin r$ .

Step 1. Write the absolute refractive index of each medium separately using the defining ratio. For medium 1, $n_1 = c/v_1$ , so $v_1 = c/n_1$ . For medium 2, $n_2 = c/v_2$ , so $v_2 = c/n_2$ . Both expressions use the same vacuum speed $c$ , since that is the one reference every medium is compared against.

Step 2. The relative refractive index of medium 2 with respect to medium 1 is defined directly as the ratio of the two speeds, $n_{21} = v_1/v_2$ , because that ratio is what tells you how much more (or less) medium 2 slows the ray down compared to medium 1 alone.

Step 3. Substitute the Step 1 expressions for $v_1$ and $v_2$ into $n_{21} = v_1/v_2$ : $n_{21} = \dfrac{c/n_1}{c/n_2} = \dfrac{c}{n_1}\times\dfrac{n_2}{c} = \dfrac{n_2}{n_1}$ . The vacuum speed $c$ cancels exactly, leaving the clean rule $n_{21} = n_2/n_1$ — relative refractive index is just the ratio of the two absolute refractive indices.

Step 4. This same $n_{21}$ is what Snell's law reports experimentally as $\sin i/\sin r$ . So measuring the bending angles at a boundary and computing $n_{21} = n_2/n_1$ from tabulated absolute values must agree — this cross-check is exactly what CBSE numericals test.

Worked example

Light travels from water ( $n_1 = 1.33$ ) into glass ( $n_2 = 1.5$ ). Find the relative refractive index of glass with respect to water, and state whether the ray bends towards or away from the normal on entering the glass.

Step 1. Identify the two absolute refractive indices from the standard reference values: water $n_1 = 1.33$ , glass $n_2 = 1.5$ .

Step 2. Apply the ratio derived above: $n_{21} = \dfrac{n_2}{n_1} = \dfrac{1.5}{1.33} \approx 1.13$ .

Step 3. Interpret the result. Since $n_{21} > 1$ , glass is optically denser than water, so light travels slower in glass. Going from a rarer medium (water) into a denser one (glass), the ray bends towards the normal. Snell's law confirms this: $\sin i/\sin r = n_{21} \approx 1.13 > 1$ forces $\sin r < \sin i$ , hence $r < i$ .

The relative refractive index of glass with respect to water is $n_{21} \approx 1.13$ , and the ray bends towards the normal.

Common traps

Confusing "optically denser" with mass density. A higher refractive index means slower light, not necessarily a heavier substance — the two ideas often correlate but are not the same thing.
Inverting the ratio in $n = c/v$ . It is vacuum speed over medium speed, never the other way round — flipping it would give $n < 1$ for a real medium, which cannot happen.
Forgetting absolute $n$ is always at least $1$ . Only relative refractive index between two media can be less than $1$ (when light goes from a denser medium into a rarer one).
Treating refractive index as fixed regardless of pairing. Absolute refractive index (versus vacuum) is one fixed number per substance; relative refractive index changes depending on which two media are being compared.
Mixing up which angle is which in Snell's law. The angle of incidence $i$ and angle of refraction $r$ are both measured from the normal, not from the boundary surface — swapping this reference line is a common source of a wrong final answer even when the refractive index itself is computed correctly.

Ask the tutor: If the jump from absolute to relative refractive index, or how either connects to Snell's law, still feels shaky, ask the AI tutor to walk through two or three more medium pairs with you.

Why is refractive index always greater than or equal to 1 for a single medium, but relative refractive index can be less than 1?

Absolute refractive index compares a medium's light speed to the speed in vacuum, which is the fastest light can ever travel, so $v \leq c$ forces $n = c/v \geq 1$ always. Relative refractive index, however, compares two ordinary media to each other, and if you go from a denser medium into a rarer one, $n_{21} = n_2/n_1$ can easily come out below $1$ — for example glass into water gives $1.33/1.5 \approx 0.89$ .

If diamond has such a high refractive index, does that mean light travels through it very slowly?

Yes, relatively speaking. Using $n = c/v$ , diamond's $n \approx 2.42$ means $v = c/2.42 \approx 1.24\times10^8\ \text{m/s}$ , less than half the speed of light in vacuum, and noticeably slower than in water or glass. That extra slowing is exactly why diamond bends light so strongly and produces such vivid sparkle when cut.

How is refractive index actually connected to Snell's law in a numerical problem?

Snell's law states $\sin i/\sin r = n_{21}$ , where $n_{21}$ is the relative refractive index of the second medium with respect to the first. If a question gives you the absolute refractive indices of the two media instead of angles, compute $n_{21} = n_2/n_1$ first, then use that same number inside Snell's law to find an unknown angle, or vice versa.

Refractive index

The core idea

Worked example

Common traps

Before this

Where this leads