Assertion (A): Propagation of light through an optical fiber is due to total internal reflection taking place at the core-cladding interface.
Reason (R): Refractive index of the material of the core of optical fiber is greater than that of air.
A. Both (A) and (R) are true and (R) is the correct explanation of (A).
B. Both (A) and (R) are true but (R) is not the correct explanation of (A).
C. (A) is true and (R) is false.
D. (A) is false and (R) is true.

Hint: Propagation of light through an optical fiber is due to total internal reflection taking place at the interface of cable and air (surrounding atmosphere). In this case, the refractive index of cable is such that light always has total internal reflection and the refractive index of the material of the cable of the optical fiber is greater than that of the air.

Complete step by step answer:
Optical fiber is a flexible and transparent medium made of glass or plastic having a cylindrical shape thicker than that of human air. The fiber consists of three sections: The core, the cladding and the jacket. Outer portion of fiber is jacket; innermost is core which is covered by the cladding then jacket.

The refractive index of the glass core is${{n}_{1}}$ and that of the cladding layer is ${{n}_{60231250}}$. The refractive index of the glass core $\left( {{n}_{1}} \right)$ is always higher than that of cladding layer $\left( {{n}_{60231250}} \right)$ i.e. ${{n}_{1}}>{{n}_{60231250}}$ .The light enters into the glass fiber from one end with an angle of incidence $\Phi $. This angle $\Phi $ should be the greater than an angle ∅c called as critical angle. When the light enters into the glass core at angle $\Phi $, it bends away from the cladding because refractive index of cladding $\left( {{n}_{60231250}} \right)$ is lower than that of the glass core$\left( {{n}_{1}} \right)$. This ray travels towards the other side of the glass core where it again bends away from the cladding. This process is called total internal reflection and it is demonstrated in the above figure. The light enters into a glass fiber from one end, and gets reflected severally within the fiber. It follows a zigzag path along the length of the fiber.
When the light enters into a glass fiber from one end, most of it propagates along the length of the fiber and comes out from the far end. The light stays inside the fiber and does not escape through the walls because of the total internal reflection of the light inside the fiber. This total internal reflection takes place only if the following two conditions are satisfied.
Refractive index $\left( {{n}_{1}} \right)$ should be higher than that of the cladding$\left( {{n}_{60231250}} \right)$. So, as you can see, this is the reason for assertion (A) but the statement given in reason (R) is also true but (R) is not the correct explanation of (A).

So, the correct answer is “Option B”.

Note: There is one more condition for the total internal reflection which is, the angle of incidence \[\left( {{\Phi }_{1}} \right)\] of the light entering the fiber should be greater than the critical angle \[\left( {{\Phi }_{C}} \right)\]. The light which travels from one end to the other end of the glass fiber is said to have guided through the fiber. The sources used to propagate through fiber are generally laser or LED light (monochromatic light).