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# Total Internal Reflection- Optical Fiber

## Ray Theory Transmission

Let’s see what happens when a light ray encounters a boundary separating two different media? In the figure given below, n1 and n2 are the refractive indices of the two media. Here n1 & n2 represents the denser and rare mediums respectively. The incident light ray strike at the point where a normal which is perpendicular to the plan is drawn. Here, Phi 1 ($\phi_{1}$ ) denotes the incident angle for different incident rays and Phi2 ($\phi_{2}$) for the refracted rays.  These angles are considered with respect to the normal, in both the cases incident as well as refracted.

The reflection and refraction of a light ray at a material boundary. The relationship between angles and refractive indices of the two media can be established by using the Snell’s law.

So applying Snell’s law at the boundary, we get

$n_{1}&space;sin\phi_{1}=n_{2}sin\phi_{2}$

$n_{1}cos\theta_{1}=n_{2}cos\phi_{2}=n_{2}cos\theta_{2}$

$\phi_{1}$ =Angle of incidence

$\phi_{2}$ = Angle of refraction

## Observe:

There are three incident rays (Red, Blue, and Green) in the above picture, for the first incident ray Red, see the refraction, it is away from the normal or towards the normal. It is away from the normal because the second medium is rare.

Now see the Blue-ray, the incident angle increases for this ray and as a result, it deviates more than Red in the second medium. If continuously incident angle increases as you can see for the Green light ray, it deviates comparatively more from the earlier cases.

If the refracted ray deviates by ninety degrees at a specific incident angle as shown in the Green Light Ray case, then the incident angle is called the Critical Angle. This is called limiting case of refraction. Beyond that light will reflect in the same medium. Mathematically,

$\inline&space;\phi&space;_{1}=\phi&space;_{c};&space;\phi&space;_{2}=90^{0}$

Total Internal Reflection takes place when,

$\phi&space;>&space;\phi&space;_{c}$

So, now Snell’s law of refraction (at the limiting case),

$n_{1}sin\phi&space;_{1}=n_{2}sin\phi&space;_{2}$

$\inline&space;\phi&space;_{1}=\phi&space;_{c};&space;\phi&space;_{2}=90^{0}$

$n_{1}sin\phi&space;_{c}=n_{2}sin90$

$Sin\phi_{c}=\frac{n_{2}}{n_{1}}$

This is Limiting case of refraction to find the critical angle.

## After reading the topic attempt this quiz:

Total Internal reflection of light ray inside the core of an optical fiber is the only way by transmitting the signal. How it happens and what is the condition for that. Just check here..

1. Do you think that Total Internal Reflection is the only principle by which light can travels inside the core?

2. What is the use of Snell’s Law?

3. What is the critical angle?

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