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Refraction Through a Slab

Shine the torch through a slab of water, glass or diamond, and make it thicker or thinner.

Airlight: 300,000 km/sGlasslight: 200,000 km/sAirlight: 300,000 km/s45°28°45°shift

In, through and out: the light bends towards the normal as it goes into the slab, and bends back just as much as it comes out. It leaves going the same way as before, only shifted to one side.

Angle going in
45°
Angle inside the slab
28°
Angle coming out
45°
Shifted sideways by
39 mm
Slab

What’s happening

In Refraction light bends as it goes into water, glass or diamond. Here it has to come out again, through the slab’s bottom face, which is parallel to the top. Going in, the light bends towards the normal (the line standing straight up from the surface); coming out, it bends away from it by exactly the same amount. The two bends cancel: the light leaves going the same way it came in, but shifted to one side. A thicker slab, a more slanted torch or a material that slows light more all make the shift bigger.

Try this

  • Find the angle where the light shifts the most.
  • Pick diamond, then make the slab twice as thick. Which changed the shift more?
  • Is the light that comes out ever not parallel to the light going in?
  • At home: look at a pencil through the edge of a thick glass or a jar of water, then tilt it. Does the pencil seem to jump?
Learn more: two bends, the size of the shift, and why pools look shallow

Two bends. At the top face the light goes from air into the slab. With θ1\theta_1 the angle going in and θ2\theta_2 the angle inside (both measured from the normal), Snell’s law says how much it bends:

n1sin⁡θ1=n2sin⁡θ2n_1 \sin\theta_1 = n_2 \sin\theta_2

At the bottom face the same thing happens the other way round, from the slab back into air. The light inside meets the bottom face at θ2\theta_2 too, because the faces are parallel, so it comes out at an angle θ3\theta_3 that has to equal the angle it went in at:

n2sin⁡θ2=n1sin⁡θ3⇒θ3=θ1n_2 \sin\theta_2 = n_1 \sin\theta_3 \quad\Rightarrow\quad \theta_3 = \theta_1

How big the shift is. For a slab of thickness tt, the light that leaves runs parallel to where it was heading, a distance dd to one side:

d=t sin⁡(θ1−θ2)cos⁡θ2d = \frac{t \, \sin(\theta_1 - \theta_2)}{\cos\theta_2}

Head on, the two angles are both 0 and there is no shift. The more slanted the light, the bigger the gap between θ1\theta_1 and θ2\theta_2, and the longer its slanted path through the slab, so the shift grows quickly. Doubling the thickness doubles it.

Things look closer. Looking straight down through a slab of glass with refractive index n, things underneath look nearer than they really are:

raised by    t(1−1n)\text{raised by} \;\; t\left(1 - \frac{1}{n}\right)

For glass (n = 1.5), a 6 cm paperweight lifts the words under it by 2 cm, which is why they seem to float inside it.

If the faces aren’t parallel, the two bends no longer cancel, and the light comes out going a new way. That is a prism, and a lens is a glass whose faces tilt more and more towards its edges.

  • Windows: a window pane shifts what you see through it a tiny bit; thick glass, seen at a slant, shifts it more.
  • Aquariums: the fish near the sides of a tank are not quite where they seem, because you see them at a slant through the thick glass and the water.
  • Swimming pools: the water lifts the bottom of the pool, so it looks shallower than it is.
  • Scientific instruments: a tilted glass plate is put in a beam of light on purpose to move it sideways without turning it.

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