Optics Question 127

Question: An optical fibre consists of core of m­1 surrounded by a cladding of m2 < m1. A beam of light enters from air at an angle a with axis of fibre. The highest a for which ray can be travelled through fibre is

Options:

A) cos1μ22μ12

B) sin1μ12μ22

C) tan1μ12μ22

D) sec1μ12μ22

Show Answer

Answer:

Correct Answer: B

Solution:

Here the requirement is that i>c

sini>sincsini>μ2μ1 …(i) From Snell’s law μ1=sinαsinr ..(ii) Also in ΔOBA

r+i=90o

r=(90i) Hence from equation (ii) sinα=μ1sin(90i)

cosi=sinαμ1

sini=1cos2i

=1(sinαμ1)2 ..(iii) From equation (i) and (iii) 1(sinαμ1)2>μ2μ1

Therefore sin2α<(μ12μ22)

Therefore sinα<μ12μ22

αmax=sin1μ12μ22



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