### Total Internal Reflection Formula :

Total internal Reflection formula is the refractive index in medium n_{1 } and divided by the refractive index in medium 2 n_{2} is equal to the angle of refraction sin r and divided by the angle of incidence sin i. Hence the Total internal Reflection formula can be written as

Total internal reflection n_{1}/n_{2} =sin r / sin i

Critical angle θ =Sinθ =n_{2} /n_{1}

R → angle of refraction

I→ angle of incidence

n_{1} → refractive index in medium 1

n_{2}→ refractive index in medium 2

θ→ critical angle

### Example:1

### Answer:

An optical fiber made up the glass with refractive index n1=2.5 which is surrounded by another glass of refractive index n_{2} of the cladding such that the critical angle between the two cladding is 90^{0}

### Answer:

Ciritical angle θ =90^{0}

Refractive index n1=2.5

Refractive index n2=?

Using the below formula we can calculate n2

Sin θ =n_{2} /n_{1}

Sin 90^{0} =n2/ 2.5

N2=2.5* sin 90^{0}

N2=2.10

### Example:2

Calculate the refractive index of the medium whose critical angle 30^{0 }?

### Answer:

Critical angle θ=30^{0}

Refractive index of the medium μ=?

μ =1/ sin θ

μ =1/ sin 40^{0}

μ=1/0.8414

μ=0.84