TE Enriched Sample (E)

Endoscopy Checkpoint 6 77 2.3 The refractive indices of the core and the cladding in an optical fibre are 1.49 and 1.47, respectively. cladding core c air θ max (a) What is the critical angle at the core–cladding boundary? (b) What is the maximum entrance angle θ max at the end so that light can be guided along it? Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) The critical angle c can be found by . . . . ° sin c n n c 1 49 1 47 80 602 80 6 ° 1 2 ` . = = = (b) For the maximum entrance angle, the angle of refraction at the air–core boundary is 90° − 80.602° = 9.398°. Applying Snell’s law, we have . . . ° . ° sin sin 1 1 49 9 398 14 08 14 1 ° max max # # . i i = = What-if . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Will the maximum entrance angle increase or decrease if the optical fibre is immersed in water? Q&A Q: Compare the critical angle at the core–air boundary ( α ) and that at the core–cladding boundary ( β ). Which is larger? A: The critical angle β (at cladding boundary) is larger as the refractive index difference between the core and the cladding is smaller than that between the core and the air. Ss may wonder why a cladding is used despite that it increases the critical angle (decreases θ max ). Without the cladding, a light ray may ‘leak’ from one fibre to another at the point of contact. The related phenomenon is called the frustrated total internal reflection. (See DSE 2021 Q4.2) air core 9.398° θ max Ans: decrease Maximum entrance angle Example 2.6 ` 1. State two criteria for total internal reflection to occur. 2. The refractive indices of the core and the cladding of an optical fibre are 1.55 and 1.45, respectively. What is the critical angle θ c at the core–cladding boundary? ( ) ( ) sin c c & i i = = 1.45 1.55 69.3° 3. In an optical fibre, a light ray is incident on the core–cladding boundary at an angle smaller than the critical angle. Will the following happen? (a) The light ray will completely leak to the cladding. (b) Part of the light ray is reflected. (c) The reflected light ray, if any, makes an angle θ with the normal such that θ is larger than the angle of incidence. F T F ( MC: DSE 2018 Q4.5, 2021 Q4.2) Sample © United Prime Educational Publishing (HK) Limited, Pearson Education Asia Limited 2023 All rights reserved; no part of this publication may be reproduced, photocopied, recorded or otherwise, without the prior written permission of the Publishers.