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Refraction and Internal Reflection

Watch this to understand refraction and internal reflection (and where to look for the gold)

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Rainbows. The stuff of unicorns, fairies and pots of gold.

They hypnotise kids simply because they seem so incredibly unlikely. How can we possibly have a gigantic technicolour arc suddenly appear that stretches across the sky, which then disappears as quickly as it arrived?

No wonder it is linked to magic and dream worlds.

But the Physics that underpins rainbows is no less amazing. It makes sense to most of us, but to truly understand it, you have to know about refraction.

Let’s find some gold.

This is thinkfour.

In our rainbows there are two phenomena being exhibited. We have refraction of light as it enters our raindrop , and then total internal reflection of the light within the water droplet before the light refracts back out the side of the droplet.

Refraction of light is governed by Snell’s law. N1 sin theta1 equals N 2 sin theta 2 where n1 is the refractive index of the initial material and theta 1 is the angle of incidence. N2 is the refractive index of the second material and theta 2 is the angle of refraction.

Internal reflection occurs if the angle of incidence that the light is striking the surface at is greater than the critical angle. Critical angle can be calculated using the equation n equals 1 over sin C. Where n is the refractive index of the material the light is traveling through, and C is the critical angle.

Lets look at a challenging example of the type of question you could be asked to show how we might apply these concepts.

In this question you are given a situation where much like in our rainbow light enters a material and refracts as it does so before reflecting internally.

Part a asks us to calculate the refractive index of the glass sphere. From the question we know that n1 which is air will be equal to 1, the angle of incidence theta 1 is 36 degrees, and the angle of refraction theta 2 is 18 degrees.

In this case we will use Snell’s law to calculate n2. If we substitute our values into n1 sin theta 1 = n2 sin theta 2 we have:

1 sin (36) = n2 sin (18) or sin(36) divided by sin (18) which equals 1.90 to 3 significant figures.

Part b asks us to find the critical angle of the glass. For this we will use our second equation n= 1 over sin C.

So 1.9 = 1 over sinC which can be rearranged to C = inverse sin of 1 over 1.9. Which gives us 31.8 degrees.

So, you see, the magic of adding light with a raindrop does not need to have unicorns as part of the story.

Physics is enough. The physical principles that underpin our world are amazing and will blow your mind.

When you understand what causes what, and why rainbows work as they do, it is no less impressive. In fact, I would argue it makes for an even greater story.

It also won’t stop me from occasionally checking if there is indeed a pot of gold at the end of them.

This was thinkfour; thanks for watching.