A cylinderical optical fibre (quarter circular shape) of refractive index \[n=2\] and diameter \[d=4\text{ }mm\] is surrounded by air. A light beam is sent into the fibre along its axis as shown in figure. Then the smallest outer radius R (as shown in figure) for which no light escapes after first incident on curved surface of fibre is: |
A) 2 mm
B) 4 mm
C) 8 mm
D) 6 mm
Correct Answer: B
Solution :
[b] |
\[{{\theta }_{\min }}>C\] |
\[\sin {{\theta }_{\min }}>\sin C\] |
\[\frac{R-d}{R}>\frac{1}{n}\]\[\Rightarrow \] \[Rn-dn>R\]\[\Rightarrow \] \[R>\frac{nd}{n-1}\] |
\[R>\frac{2.4\,mm}{2-1}\] |
\[R>8\,\,mm\] |
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