question_answer

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]

\[{{\theta }_{\min }}>C\]

\[\sin {{\theta }_{\min }}>\sin C\]

\[\frac{R-d}{R}>\frac{1}{n}\]\[\Rightarrow \]          \[Rn-dn>R\]\[\Rightarrow \]    \[R>\frac{nd}{n-1}\]

\[R>\frac{2.4\,mm}{2-1}\]

\[R>8\,\,mm\]