REFRACTION

When a wave enters a different medium with different structure - eg crystalline structure different, or a glass or a covalent molecular gas, its velocity will alter.

No waves are lost, so the frequency remains constant, but the wavelength has to alter by

v = λf.

In the animation, waves are entering a medium which causes them to slow down significantly.

In slowing and changing wavelength, the angle at which they proceed MUST change - they REFRACT.

We can calculate the way in which they refract by studying the distance the waves move in one period,T, of their motion.

Remember - we cannot lose waves, so the frequency at which they pass cannot change, so their period does not change either - f = 1 / T.

In that time, all parts of the wave move one wavelength, the longer wavelength outside the medium, the shorter wavelength inside the medium.

If the velocity in the first medium is v₁, in the second, v₂, then

f = v₁ /λ₁ = v₂ /λ₂ A small amount of twiddling will give λ =vT, so referring to the enlargement of the refraction animation below;

CB = distance wave in medium 1 moves in period T = v₁T = λ₁

OA = distance wave in medium 2 moves in period T = v₂T = λ₂

θi = < normal ="

θR =

Now sinθi = CB / OB , sinθR = OA / OB

It follows that sinθi / sinθR = CB / OA = v₁T / v₂T = v₁ / v₂ = n _{med2 rel med1}

This is known as Snell's Law.

I personally find it easier to remember it as

n₁ sinθ₁ = n₂ sinθ₂

n₁ and n₂ are ABSOLUTE REFRACTIVE INDICES - that is, are relative to a vacuum.

TOTAL INTERNAL REFLECTION

( This has nothing to do with contemplating one's navel. )

The phenomenon occurs when a wave travels from higher to lower refractive index eg water to air for light. It is important in telecommunications - fibre optics makes extensive use of it, as does radio wave communication whereby waves are reflected off the ionosphere.

• When a wave moves from lower absolute refractive index to higher as above, it straightens up. The converse happens when going the other way, it bends more!
• Reflection almost always occur with Refraction. It can be minimised with interference techniques, but it is the important issue in this situation.

At a certain angle of incidence, the CRITICAL ANGLE, Snell's Law gives the angle of refraction as 90⁰.

TOTAL INTERNAL REFLECTION BEGINS AT THIS POINT and for all larger incident angles.

By Snell's law,

n₁ sinθ_c = n₂ sin90⁰ = n₂, thus sinθ_c = n₂ / n₁