Paragraph: Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n₁ surrounded by a medium of lower refractive index n₂ . The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n₁ and n₂ as shown in the figure. All rays with the angle of incidence i less than a part

Step-by-step solution

Let the whole structure is placed in a medium of refractive index n ′ , then n ′ sin ⁡ i = n 1 cos ⁡ 90 - θ n ′ sin ⁡ i = n 1 c o s θ .....(i) Here for i m ; θ = C and sin ⁡ C = n 2 n 1 From equation (i), n ′ sin ⁡ i m = n 1 1 - n 2 2 n 1 2 = n 1 2 - n 2 2 ⇒ sin ⁡ i m = n 1 2 - n 2 2 n ′ Now, for (i) N A s 1 = 3 4 45 16 - 9 4 = 3 4 × 3 4 = 9 16 N A s 2 = 3 15 16 64 25 - 49 25 = 3 15 16 1 5 15 = 9 16 For (ii) N A s 1 = 15 6 × 3 4 = 15 8 N A s 2 = 3 4 = 15 5 Not equal For (iii) N A s 1 =