Total Internal Reflection?

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Total Internal Reflection?

Could somebody please explain the entirety of Total Internal Reflection in regards to the CIE O level syllabus? I usually use miniphysics.com for help, but even their notes are too difficult for me to comprehend. Please help! Thanks!

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Answer 1 · 2016-04-22T20:27:55

Snell's law helps to understand this.

Explanation:

Snell's law tells us how light behaves when it goes from one medium into another.
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In the above, Snell's law tells us that :
$n_{1} {sin θ}_{1} = n_{2} {sin θ}_{2}$ $n_1sintheta_1=n_2sintheta_2$

If light is travelling from one medium to a medium with a lower refractive index (or put another way, from one medium to a less optically dense medium) then $n_{1} > n_{2}$ $n_1>n_2$

By Snell's law then $θ_{2} > θ_{1}$ $theta_2>theta_1$ (following the maths of Snell's law)

If you increase the angle of incidence, $θ_{1}$ $theta_1$ eventually $θ_{2}$ $theta _2$ will increase until it is reflected along the boundary. At this point $θ_{2}$ $theta_2$ is $90^{0}$ $90^0$ (the critical angle).

Beyond this, and the ray will be reflected - this is total internal reflection.

For example, if medium 1 is glass ( $n_{1} = 1.55$ $n_1=1.55$ ) and medium 2 is a vacuum ( $n_{2} = 1$ $n_2=1$ )

We can see that $θ_{2} = 90^{0}$ $theta_2=90^0$ occurs when:

$1.55 \cdot sin (θ_{1}) = 1 \cdot sin (90^{0})$ $1.55*sin(theta_1)=1*sin(90^0)$
hence
$sin (θ_{1}) = \frac{1}{1.55}$ $sin(theta_1)=1/1.55$
$θ_{1} = 40^{0}$ $theta_1=40^0$
Hence when $θ_{1} > 40^{0}$ $theta_1>40^0$ the ray is reflected (total internal reflection)

If you try $θ_{1} = 41^{0}$ $theta_1=41^0$ then
$1.55 \cdot sin (41) = 1 \cdot sin (θ_{1})$ $1.55*sin(41)=1*sin(theta_1)$
$1.02 = sin (θ_{1})$ $1.02=sin(theta_1)$
And $θ_{1}$ $theta_1$ cannot be solved. Does this help?!

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Total Internal Reflection?

Could somebody please explain the entirety of Total Internal Reflection in regards to the CIE O level syllabus? I usually use miniphysics.com for help, but even their notes are too difficult for me to comprehend. Please help! Thanks!

1 Answer

Explanation:

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