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The following figure shows a cross-section of a ‘light pipe’ made of a glass fiber 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 the following phenomena to occur.  

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(i) 0 < 𝑖 < 90° 

(ii) 0 < 𝑖 < 60° 

(iii) 0 < 𝑖 < 45° 

(iv) 0 < 𝑖 < 30°

Answer

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Transcript

Question 12 (Choice 2) (e) The following figure shows a cross-section of a ‘light pipe’ made of a glass fiber 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 the following phenomena to occur. (i) 0<𝑖<90° (ii) 0<𝑖<60° (iii) 0<𝑖<45° (iv) 0<𝑖<30° 0<𝑖<60°, 1_(𝜇_2 )=1/(𝑠𝑖𝑛𝐶^′ ) 𝑠𝑖𝑛𝐶^′=1,44/1,68 0<𝑖<60°, 1_(𝜇_2 )=1/(𝑠𝑖𝑛𝐶^′ ) 𝑠𝑖𝑛𝐶^′=1,44/1,68 = 0.8571 𝐶^′=59° Total internal reflection will occur if the angle 𝑖^′>〖𝑖′〗_𝑐 , i.e., if 𝑖^′>59° or when 𝑟<𝑟_𝑚𝑎𝑥′ where 𝑟_𝑚𝑎𝑥=90°−59°=31° Using Snell’s law, (𝑆𝑖𝑛 𝑖_𝑚𝑎𝑥)/(𝑆𝑖𝑛 𝑟_𝑚𝑎𝑥 )=1.68 Or 𝑆𝑖𝑛 𝑖_𝑚𝑎𝑥=1.68 ×sin⁡〖𝑟_𝑚𝑎𝑥 〗 =1.68×sin⁡〖31°〗 =1.68×0.5150 =0.8662 ∴ 𝑖_𝑚𝑎𝑥=60° Thus all incident rays which make angles in the range 0 < i < 60° with the axis of the pipe will suffer total internal reflections in the pipes.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.