The index of refraction of the core of a typical fiber optic is n_{core} core = 1.51; the cladding has n_{clad} clad = 1.43. Calculate the critical angles for the total internal reflection i_{crit}i crit and α_{crit}α crit .

Critical angle can be defined as the incidence angle which results in the refraction angle being equal to [tex]90^{\circ}[/tex] at that angle of incidence.

For Total Internal Reflection to occur, the incidence angle must be greater than the critical angle.

Now, we know that the critical angle, [tex]\theta_{cr}[/tex] is given by:

[tex]sin\theta_{cr} = \frac{n_{clad}}{n_{core}}[/tex]

[tex]\theta_{cr} = sin^{- 1}(\frac{n_{clad}}{n_{core}})[/tex]

[tex]\theta_{cr} = sin^{- 1}(\frac{1.43}{1.51}) = sin^{- 1}(0.947) = 71.27^{\circ}[/tex]

[tex]i_{cr} = \theta_{cr} = 71.27^{\circ}[/tex]

Now, for [tex]\alpha_{cr}[/tex]:

[tex]\frac{sin\gamma_{cr}}{sin\alpha_{cr}} = \frac{1}{n_{core}}[/tex]

[tex]sin\alpha_{cr}= sin(90^{\circ} - 71.27^{\circ})\times 1.51[/tex]

[tex]sin\alpha_{cr}= sin(18.734^{\circ})\times 1.51[/tex]

[tex]\alpha_{cr}= sin^{- 1}0.485 = 29.01^{\circ}[/tex]

The index of refraction of the core of a typical fiber optic is n﻿_{core} core ​ ﻿ = 1.51; the cladding has n﻿_{clad} clad ​ ﻿ = 1.43. Calculate the critical angles for the total internal reflection ﻿i_{crit}i crit ​ ﻿ and ﻿α_{crit}α crit ​ ﻿.

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The index of refraction of the core of a typical fiber optic is n_{core} core = 1.51; the cladding has n_{clad} clad = 1.43. Calculate the critical angles for the total internal reflection i_{crit}i crit and α_{crit}α crit .