Question

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. $6mm$

Answer 1

The correct option is C $8mm$

For no light to escape during the first refraction,

${\theta }_{min}>C$

Applying sine on both sides,

$\sin \left({\theta }_{min}\right)>\sin \left(C\right)$

$\frac{R-d}{R}>\frac{1}{n}$

$n\left(R-d\right)>R$

$nR-nd>R$

$nR-R>nd$

$R\left(n-1\right)>nd$

$R>\frac{nd}{\left(n-1\right)}$

Substituting the values,

$R>\frac{2\times 4}{\left(2-1\right)}$

$R>8mm$