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Old Mar 29th 2018, 01:03 PM   #1
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Derivation of Critical Angle

Hi,

I've derived the critical angle:

n1*sin(x1) = n2*sin(x2)

x1 is critical angle of incidence, call it C.

x2 is refracted at 90 degrees, therefore sinx2 = 1

so you get sinC = n2/n1.

However, in my syllabus it is written as sinC = 1/n

Can someone please explain to me how n2/n1 = 1/n, and what this 'n' might refer to?

Many thanks,

Felix
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Old Mar 29th 2018, 02:05 PM   #2
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You are both right.

Let us say that medium 2 is air and medium 1 is glass.

A good way to keep track of refractive indices is to use the following notation

Index for light from air to glass is denoted $\displaystyle _a{n_g}$

Index for light from air to glass is denoted $\displaystyle _g{n_a}$

Due to the reversibility of light


$\displaystyle _a{n_g} = \frac{1}{{_g{n_a}}}$


It is assumed when you use n that it refers to air to glass and is often quoted as the "refractive index for glass = 1.51"

So

$\displaystyle \sin \left( C \right) = \frac{1}{{1.51}} = 0.67$

Note that n=1.51 does not yield a possible value for sinC, which must be less than 1.

Total internal reflection always occurs when the ray is approaching the less dense medium from the more dense one.

does this make sense?
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Old Mar 29th 2018, 02:25 PM   #3
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Yes, that's perfect. Thank you.

How do you type those nice equations?
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Old Mar 30th 2018, 02:48 AM   #4
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Glad to help.

There is a more to 'n' than this, which comes into play when you have light passing through multiple layers but they don't include it on the syllabus these days.

I will post it if you like.

As to mathematical expressions, there are two common ways of doing this which you will need if you progress academically.

The usual coding for webpages is called HTML which stands for

HyperTextMarkupLanguage

Markup languages were used by printers to describe how to present [printed material.
Additional to the written material, they contain embedded instructions which don't show.

A word processor is a simple version of this.


The two methods used for Mathematical subjects are MathML and Tex or LaTex.


The good news is that there are free online editors for these where you choose symbols from a chart and assemble your formulae on the screen in front of you and then copy and paste into your document or a website like this one.

Here are a couple of good sites.

Online Latex Equation Editor - Sciweavers

https://www.codecogs.com/latex/eqneditor.php

I suggest you experiment here with them.
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