Question

(a) Figure shows a cross–section of a ‘light pipe’ made of a glass fibre of refractive index 1.68. The outer covering of the pipe is made of a material of refractive index 1.44. What is the range of the angles of the incident rays with the axis of the pipe for which total reflections inside the pipe take place, as shown in the figure?  

(b) What is the answer if there is no outer covering of the pipe?

Answer 1

(a) Refractive index of outer covering, n₁ = 1.44 

Refractive index of glass fibre, n₂ = 1.68 

At the interface of the glass fibre and covering 

As, n  = n₂/n₁.

Also the critical angle, sini'_c = 1/n(i'_c critical angle)

(b) If there were no outer covering of the pipe, for air n₁ = 1, for glass fibre n₂ = 1.68

∴ i′ = 90° – 36.5° = 53.5°, 

Which is greater than i′_c . therefore all incident rays (in range 53.5° < i < 90°) will undergo total internal reflection.