GATE 2021 IN – Question 65
A large multimode fibre has $n_{core}=1.5$ and $n_{clad}=1.2$. A section with cladding removed passes through a liquid of index $n_{liquid}$. An LED illuminates one end; paper is placed 1 cm from the other. Its spot radius is 1 cm. The liquid index is ______ (two decimal places).
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Correct answer: 1.30 to 1.35
Explanation
The spot radius and fibre-to-paper distance are both 1 cm, so the emerging half-angle is θ=45°. In air, numerical aperture is sinθ=√(ncore²−nliquid²).
Therefore nliquid=√(1.5²−sin²45°)=√(2.25−0.5)=√1.75=1.322876, rounded **1.32**. This exceeds the intact cladding index 1.2, so the exposed liquid section limits the guided cone.