| A cylindrical optical fibre (quarter circular shape) of refractive index n = 2 and diameter d = 4mm 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 during first refraction from curved surface of fibre is: |
 |
A) 2mm
B) 4mm
C) 8mm
D) 6mm
Correct Answer: C
Solution :
| \[{{\theta }_{\min }}>C\] |
| \[\sin {{\theta }_{\min }}>\sin C\] |
| \[\frac{R-d}{R}>\frac{1}{n}\]\[\Rightarrow \]\[Rn-dn>R\]\[\Rightarrow \]\[R>\frac{nd}{n-1}\] |
 |
| \[R>\frac{2.4mm}{2-1}\] |
| \[R>8mm\] |
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