A Coin at the Bottom of a Bucket Is Not Where You See It

Because the light leaving the coin changes direction as it escapes the water, and your eye assumes it travelled in a straight line the whole way.

Your brain traces the rays it receives straight backwards. Those rays bent at the water surface, so the backward trace arrives at a point above the coin. You see a perfectly sharp image in exactly the wrong place.

The same effect makes a straw in a glass look broken at the surface, and a shallow pond look shallower than it is. This page covers the third part of the ICSE Class 8 Physics chapter on light: refraction, the refractive index, a ray crossing a glass block, and how a prism splits white light apart.

Refraction is the change in direction of light when it passes from one transparent medium into another.

It happens because light travels at different speeds in different media. The speed drop at the boundary is what turns the ray.

The two rules of direction:

- Going from a rarer medium into a denser one — air into glass or water — the ray slows down and bends towards the normal. So $\angle r<\angle i$.
- Going from a denser medium into a rarer one — glass or water into air — the ray speeds up and bends away from the normal. So $\angle r>\angle i$.

Here denser means optically denser, which is about the speed of light in the material and not about how heavy it feels. Cooking oil is lighter than water yet optically denser.

The one exception. A ray travelling along the normal — striking the surface at $90^{\circ }$ to it — does not bend at all. It still slows down, but with $\angle i=0^{\circ }$ there is no direction to turn towards, so $\angle r=0^{\circ }$.

That exception is a useful test of understanding: refraction is about a change of speed causing a change of direction, and when the ray meets the surface squarely the change of speed happens with no bending to show for it.

A helpful picture. Imagine a marching column crossing from a hard road onto soft sand at an angle. The rank that reaches the sand first slows first, so the whole column swings round. Light does the same at a boundary, for the same reason.

Because it bends twice, by equal amounts, in opposite senses.

Follow a ray through a rectangular glass block.

- Entering at the top face, air to glass: it bends towards the normal, so $\angle r_1<\angle i_1$.
- Travelling inside: a straight line, since the medium is uniform.
- Leaving at the bottom face, glass to air: it bends away from the normal, so $\angle r_2>\angle i_2$.

The two faces of a rectangular block are parallel, so their normals are parallel too. The bending inwards at the first face is undone exactly by the bending outwards at the second, and the emergent ray is parallel to the incident ray.

But it is not on the same line. It has been shifted sideways. That sideways shift is the lateral displacement — the perpendicular distance between the original path and the emergent ray.

What lateral displacement depends on:

- Thickness of the block — a thicker block shifts the ray more
- Angle of incidence — a larger angle shifts it more
- Refractive index — a higher index shifts it more

And it becomes zero when the ray enters along the normal, since then there is no bending at either face to shift anything.

Why the block is a good experiment. Because the emergent ray is parallel to the incident one, you can measure $\angle i$ and $\angle r$ at the first surface with a protractor and find $n$ from Snell's law without needing any equipment more complex than pins and paper.

Compare it with a prism. A prism's two refracting faces are not parallel, so its second bend does not cancel the first. The ray comes out genuinely deviated, turned through a real angle — which is exactly what makes the next section possible.

Because white light is a mixture, and the glass bends each colour by a different amount.

Dispersion is the splitting of white light into its component colours. Pass a narrow beam of sunlight through a glass prism and a band of colours appears on a screen — the spectrum.

The order, from the least bent to the most bent:

- V — violet
- I — indigo
- B — blue
- G — green
- Y — yellow
- O — orange
- R — red

remembered as VIBGYOR. On the screen red appears at the top of the band and violet at the bottom, because red is deviated least and violet most.

Why the colours separate. The refractive index of glass is not quite the same for every colour. It is slightly larger for violet than for red, so violet travels slightly more slowly inside the glass and is bent through a larger angle. Each colour therefore leaves the prism on its own path, and by the time they reach the screen they have spread apart.

Why a rectangular block cannot do this. A block does separate the colours slightly inside the glass, but its parallel faces then bend each colour back by the same amount and recombine them. Only the non-parallel faces of a prism let the separation survive to the far side.

And the reverse works too. Place a second, inverted prism after the first and the colours are brought back together into white light. That is the strongest evidence that the prism is separating something already present rather than adding colour of its own.

Where you see it outside a laboratory. A rainbow, where countless raindrops act as tiny prisms; the colours on a soap film; and the flash of colour from the edge of a thick glass pane in sunlight.