JEE Main 2022 · Physics · Ray and Wave Optics · medium

In an optical fibre the core has refractive index 1.3 and the cladding has refractive index 1.2. Light from air enters the flat end face of the fibre…

Single correct option

In an optical fibre the core has refractive index

1.3

and the cladding has refractive index

1.2

. Light from air enters the flat end face of the fibre at an angle of incidence

i

to the axis and must undergo total internal reflection at the core-cladding boundary. The maximum value of

i

Show answer and solution

Answer: (A) $30^\circ$

Let the refraction angle at the end face be

r

. The ray strikes the core-cladding boundary at angle of incidence

90^\circ-r

, which must be at least the critical angle

C

with

\sin C=\dfrac{1.2}{1.3}

. So

\cos r\ge\dfrac{12}{13}

, giving

\sin r\le\dfrac{5}{13}

. Snell's law at the end face:

\sin i=1.3\sin r\le1.3\times\dfrac5{13}=0.5

, so

i_{max}=30^\circ

. Equivalently

\sin i_{max}=\sqrt{\mu_1^{2}-\mu_2^{2}}=\sqrt{1.69-1.44}=0.5

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