The Sky Is Blue for the Same Reason a Sunset Is Red

Send a narrow beam of sunlight through a rectangular glass slab and it comes out parallel to the way it went in, shifted sideways but still white. Send the same beam through a triangular glass prism and it comes out bent — and spread into a band of colours.

Both are made of the same glass and both bend the light twice. The difference is the shape.

- In a slab the two surfaces are parallel, so the bending at the second surface exactly undoes the bending at the first, and the ray emerges in its original direction
- In a prism the two refracting surfaces are inclined to each other, so the two bendings do not cancel. They add, and the ray is turned through an angle

Once the light is being turned, a second effect becomes visible. Each colour is bent by a slightly different amount, and what was a single white beam becomes a fan of colours. The colours were there all along; the prism has simply separated them.

That same separation, performed by water droplets and by the molecules of the air, accounts for a rainbow, for the blue of the sky, for the red of a sunset, and for the twinkling of a star. The whole of the second half of this chapter is one geometrical fact applied to the atmosphere.

This page covers the second part of the CBSE Class 10 Science chapter on the colourful world: refraction through a prism, dispersion and recombination, atmospheric refraction, and the scattering of light.

Four angles, and the marks are for placing them correctly rather than for calculating anything.

- **The angle of the prism, $A$ — the angle between the two refracting surfaces
- The angle of incidence, $i$ — between the incident ray and the normal at the first surface
- The angle of refraction, $r$ — between the refracted ray inside the glass and that same normal
- The angle of emergence, $e$ — between the emergent ray and the normal at the second surface
- The angle of deviation, $D$ — between the direction of the incident ray produced forward and the direction of the emergent ray

The path of the ray, step by step.

- At the first surface the ray goes from air into glass, a rarer to a denser medium, so it bends towards** the normal and $r<i$
- It travels in a straight line through the glass
- At the second surface it goes from glass into air, denser to rarer, so it bends away from the normal and $e$ is larger than the angle inside
- Because the surfaces are not parallel, the two bendings do not cancel, and the emergent ray makes an angle $D$ with the original direction

The relation that connects them all:

$$i+e=A+D$$

Worked example. A ray falls on a prism of angle $60^{\circ }$ at an angle of incidence of $45^{\circ }$, and emerges at $45^{\circ }$. Find the angle of deviation.

$$D=i+e-A=45^{\circ }+45^{\circ }-60^{\circ }=30^{\circ }$$

**Notice that $i$ and $e$ came out equal here. That is the special case in which the deviation is at its minimum, and it is the arrangement in which the ray passes symmetrically through the prism. Increase or decrease $i$ from that value and $D$ gets larger, which is a result worth knowing because it is examined in Class 11.

Worked example 2 — an unequal case.** For the same prism, a ray enters at $i=60^{\circ }$ and emerges at $e=32^{\circ }$. Then

$$D=60^{\circ }+32^{\circ }-60^{\circ }=32^{\circ }$$

which is larger than the $30^{\circ }$ above, as the minimum-deviation result requires.

The comparison with the glass slab is the point to state in an answer. A slab gives lateral displacement with no deviation; a prism gives deviation. Parallel surfaces cancel the bending and inclined surfaces accumulate it, and that single sentence answers any question about why the two behave differently.

One detail about the labelling. The angle of deviation is measured between the produced incident ray and the emergent ray, not between the incident ray and the surface. Drawing the incident ray's continuation as a dotted line first makes the angle obvious and is what the marking scheme expects.

Because each colour has a slightly different refractive index in glass, so each is deviated by a different amount. Red bends least and violet most.

Pass white light through a prism and a band of colours appears on a screen, in the order

$$\text{violet, indigo, blue, green, yellow, orange, red}$$

from the most deviated to the least. That band is a spectrum, and the splitting is called dispersion.

Why the colours separate. Refractive index depends slightly on colour, because the different colours travel at slightly different speeds in glass. Violet travels slowest in glass, so it has the highest refractive index and is bent most; red travels fastest, so it is bent least. The prism is not adding anything — it is sorting what white light already contained.

How to prove that nothing was added: recombination. Place a second, identical prism upside down next to the first. The second prism deviates every colour by the same amount in the opposite direction, so the fan closes up again and white light emerges.

That experiment settles the question completely. If the prism had created the colours, a second prism could only have created more. Getting white light back proves that the colours were present in the original beam and were merely separated.

A rainbow is the same effect performed by water. Sunlight falls on tiny water droplets suspended in the air after rain, and each droplet:

- Refracts the light as it enters, splitting it
- Reflects it internally off the far side of the droplet
- Refracts it again as it leaves, splitting it further

So each droplet is a tiny prism, and the combined effect of very many of them is an arc of colour. A rainbow is always seen in the direction opposite the sun — with the sun behind you and the rain in front — which follows directly from the internal reflection sending the light back the way it came.

A second observation from the same cause. A beam of white light passing through a prism made of a more dispersive glass gives a wider spectrum, because the difference between the red and violet refractive indices is larger. Dispersion depends on the material, not only on the shape, which is why lens designers can cancel it by combining two different glasses — the point the lens chapter ended on.

The misconception to clear. The prism does not colour the light, and it does not change any colour into another. Each colour goes straight through, deviated by its own amount, and a red ray entering stays red throughout. Dispersion is a separation, not a transformation.

Because the atmosphere is not one medium but many layers of different density, so light passing through it is refracted continuously and by a constantly changing amount.

The cause, stated once for all three effects. Air's refractive index depends on its density, which depends on its temperature. Hot air is optically rarer and cool air optically denser, and the atmosphere is a shifting mixture of both. So a ray travelling down through it is bent repeatedly, and the bending keeps changing as the air moves.

Twinkling of stars. A star is so far away that it is effectively a point source. Its light reaches us through all those shifting layers, so:

- The apparent position of the star wavers slightly as the refraction changes
- The amount of light entering the eye fluctuates — sometimes a little more, sometimes a little less
- The star therefore appears to flicker in brightness, which is what twinkling is

Why planets do not twinkle. A planet is much closer, so it is not a point but an extended source — effectively a large collection of point sources. Each point twinkles, but they do so independently, and the variations average out. The total light arriving stays nearly steady, so a planet shines without flickering.

That is a genuinely useful observation. A steady bright object in the night sky is probably a planet; a flickering one is a star. The physics of this section is a practical identification method.

Advance sunrise and delayed sunset. The sun's light is bent as it passes through the atmosphere, so we can see the sun even when it is still below the horizon. The effect works at both ends of the day:

- The sun becomes visible about two minutes before it actually rises above the horizon
- It remains visible about two minutes after it has actually set

So the day is lengthened by roughly four minutes compared with what it would be without an atmosphere. The sun you see at the horizon is not where the sun is, which is the same kind of apparent displacement as a coin appearing raised in a bowl of water.

And the sun looks flattened at the horizon. The light from its lower edge travels through more atmosphere than the light from its upper edge, so the two are bent by different amounts and the disc appears squashed. The flattening is strongest exactly when the sun is at the horizon, and it disappears as the sun rises.

One more version of the same effect you can see any hot afternoon. Look at something through the air just above a fire, or along a road surface in the sun, and it shimmers. The hot air rising is constantly changing the refractive index along the path, so the apparent position of whatever is behind it keeps shifting. A twinkling star and a shimmering road are the same phenomenon at different distances.

Fine particles scatter blue light much more than red, so the light you see sideways is blue and the light left after a long path is red.

What scattering is. When light passes through a medium containing very fine particles, some of it is sent off in all directions instead of continuing straight. The amount scattered depends on the size of the particles and on the colour of the light.

- Very fine particles — finer than the wavelength of light — scatter blue strongly and red weakly
- Larger particles scatter all colours more or less equally

The Tyndall effect. When a beam of light passes through a medium with suspended particles, the beam's path becomes visible because scattered light reaches your eye from along it. You see it when:

- A fine beam of sunlight enters a dark room through a small hole and lights up the dust in the air
- Sunlight comes through the canopy of a dense forest and the shafts become visible
- A beam passes through a smoky room or through a suspension in water

The blue sky. The molecules of the air and other very fine particles are smaller than the wavelength of visible light, so they scatter the blue end of the spectrum far more than the red. That scattered blue light reaches your eyes from every direction in the sky, which is why the sky looks blue rather than showing the sun's white light only where the sun is.

And the test of that explanation. To an astronaut above the atmosphere the sky appears black, because there is nothing there to scatter the sunlight. No atmosphere, no scattering, no blue — which is exactly what the explanation predicts.

The reddish sun at sunrise and sunset. When the sun is near the horizon its light has to travel through a much longer path of atmosphere to reach you than when it is overhead. Along that long path:

- Most of the blue light is scattered away before it arrives
- The light that survives to reach your eye is mostly red and orange

So the sun looks reddish, and the sky around it takes on the same colours. At noon the path is shortest, very little blue is removed, and the sun appears white.

Notice that the blue sky and the red sunset are the same fact seen from two directions. Looking away from the sun you see the scattered light, which is blue. Looking towards the sun through a long path you see what is left after the blue has been scattered out, which is red. One phenomenon, two views — which is what this page's title means.

Why danger signals are red. Of all the colours, red is scattered the least, so it travels furthest through fog, haze, mist and dust without being dispersed. A red light is therefore visible from a greater distance than any other colour in bad conditions, which is why it is used for stop signals, for railway warnings and for tail lights.

Why clouds are white. A cloud is made of water droplets, which are far larger than air molecules. Large particles scatter all colours about equally, so the scattered light is still white. The size of the particle, not the substance, decides the colour — and that one sentence answers the blue sky and the white cloud together.

One boundary case that ties it up. On a very dusty or polluted day the sky looks whitish rather than blue, because the larger dust particles scatter all colours. The blue of a clear sky is evidence that the air is clean, and the whitening of it is evidence that it is not.