Dispersion through a prism

White light is not one colour — it is many, superposed. Sunlight, and the light from a filament bulb, look colourless only because red, orange, yellow, green, blue, indigo and violet light are all arriving together, in roughly equal amounts, and our eyes blend them into "white." A prism does not manufacture these colours; it reveals colours that were already travelling inside the beam.

Refraction is the tool, but the amount of bending is colour-dependent. When any single ray of light crosses from air into glass, Snell's law fixes how much it bends:

where: $i$ is the angle of incidence in air, $r$ is the angle of refraction inside the glass, and $\mu$ is the refractive index of the glass for that particular ray. For a fixed angle of incidence, a larger $\mu$ forces a smaller $r$ — the ray bends more sharply toward the normal. This is the entire secret of dispersion: glass does not have one single value of $\mu$; it has a slightly different $\mu$ for each colour of light.

Refractive index rises smoothly from red to violet. Violet light has the largest refractive index in glass, red light has the smallest, and the other five colours sit in between in a fixed order. Because a larger $\mu$ means sharper bending (from the relation above), violet is bent the most as it enters and again as it leaves the prism, red is bent the least, and the five colours in between spread out smoothly according to their own refractive index. The result, after both refracting faces of the prism, is a continuous, ordered fan of colours called the spectrum, always arranged in the same sequence:

remembered by the acronym VIBGYOR, with violet at one edge of the band (bent the most) and red at the other (bent the least).

The ICSE syllabus does not require a deviation-angle formula for a prism, so the reasoning here stays purely qualitative — but it still needs to be argued carefully, since exam answers are marked on the logic, not just on stating VIBGYOR from memory. The goal is to explain, using only Snell's law and the fact that refractive index depends on colour, why the spectrum forms and why its colour order can never change.

Step 1. Start from Snell's law at the first (entry) face of the prism: $\sin i / \sin r = \mu$. A beam of white light strikes this face at one single angle of incidence $i$, because all the colours are travelling together along the same incoming ray before they enter the glass.

Step 2. Since $i$ is the same for every colour but $\mu$ differs colour by colour (largest for violet, smallest for red), the angle of refraction $r$ inside the glass must also differ colour by colour. A larger $\mu$ forces $\sin r$ to be smaller for the same $\sin i$, so $r$ is smaller — the ray bends more sharply toward the normal. Violet, with the largest $\mu$, therefore refracts at the smallest angle $r$ and follows the most sharply bent path through the glass; red follows the least-bent path.

Step 3. Inside the prism, each colour now travels along its own slightly different path toward the second (exit) face, because Step 2 has already separated their directions by a small amount. At the exit face the same argument repeats: each colour refracts again according to its own $\mu$, bending further away from where an undeviated ray would have gone. Two refractions per colour, both governed by that colour's own $\mu$, add up to a real, visible angular separation between violet and red by the time the light leaves the prism.

Step 4. Because $\mu$ increases smoothly and monotonically from red to violet across the visible colours, the amount of total bending also increases smoothly and monotonically from red to violet. This is precisely why the exiting colours are not scrambled but appear in one fixed sequence, VIBGYOR, every single time, for every ordinary glass prism — the order is a direct fingerprint of how refractive index varies with colour, not an arbitrary or memorised label.

A student shines a narrow beam of sunlight through a glass prism onto a white screen and sees a band of colour with violet at the top edge and red at the bottom edge. Explain why violet appears at one extreme and red at the other, and why the intermediate colours cannot swap places in the band.

Step 1. Identify what stays the same and what changes. Every colour in the sunlight strikes the first face of the prism at the same angle of incidence $i$, since they arrive together along one ray. What changes from colour to colour is the refractive index $\mu$ of the glass.

Step 2. Apply $\sin i/\sin r = \mu$ to the extremes. Violet light has the largest $\mu$ of all the visible colours in glass, so it gives the smallest angle of refraction $r$ and is bent the most sharply, both entering and leaving the prism. Red light has the smallest $\mu$, so it gives the largest $r$ and is bent the least.

Step 3. Place the colours in the band. The colour bent the most (violet) ends up farthest from the direction of the original, undeviated beam; the colour bent the least (red) ends up closest to it. The five remaining colours — indigo, blue, green, yellow, orange — have refractive indices that fall in strict decreasing order between violet's and red's, so they must be bent by strictly decreasing amounts, which locks them into the band in exactly that order between the two extremes.

Step 4. Conclude. Violet appears at one edge because it has the largest $\mu$ and hence the greatest total bending after two refractions; red appears at the other edge because it has the smallest $\mu$. The intermediate colours cannot swap places because their refractive indices are fixed, ordered quantities. The VIBGYOR order is a direct, unavoidable consequence of how refractive index varies with colour in glass, from violet (highest) to red (lowest).

Recombination confirms it

Newton's classic follow-up settles any doubt that the prism is "creating" colour. Pass the dispersed spectrum from the first prism through a second, identical prism held upside-down (inverted) in its path. Each colour is bent again, but now in the reverse sense, exactly undoing its earlier deviation; since the two prisms are identical, the undoing is exact, and all seven colours converge back into a single beam of white light on the screen. If the first prism had somehow generated new colours, a second prism could never restore plain white — the fact that it does proves white light already contained all of VIBGYOR, and the prism's only role is to separate colours, never to create them.

• Saying the prism "adds" or "creates" colour — it only separates colours already present in white light; recombination with a second, inverted prism proves this.
• Getting the VIBGYOR order backwards, or forgetting that violet (not red) bends the most — check by remembering violet has the highest refractive index.
• Assuming refractive index is a single fixed number for glass — dispersion exists precisely because $\mu$ varies (however slightly) from colour to colour.
• Trying to compute a numeric angle of deviation for the prism — ICSE treats this topic qualitatively only; no deviation-angle formula is expected in this chapter.

Ask the tutor: Want to connect dispersion to how rainbows form in raindrops, or to the wave nature of light that explains why shorter wavelengths bend more?