CBSE Class 12 Sample Paper for 2022 Boards [Term 2] - Physics

Question 12 (Case Study) - (e) - CBSE Class 12 Sample Paper for 2022 Boards [Term 2] - Physics - Solutions to CBSE Sample Paper - Physics Class 12

Last updated at March 29, 2022 by Teachoo

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°

Answer

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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.

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.