Question

Monochromatic light from a step tad $(n_1=1.500;n_2=1.485)$, multimode optical fiber of core diameter $100\mu \text{m}$ is incident through air ($n=$ 1.000) onto a linear photo-detector array placed at $1\text{mm}$ distance from the tip of the fiber. The tip of the fiber is polished and its exit plants perpendicular to the axis of the fiber. The detect array is oriented parallel to the exit plane of tip. The array consists of photo-detector elements each of 5 pm diameter. The distance between the edges of two adjacent elements can be assumed to be zero. The number of elements illuminated by the light coming out of the fiber is

• A. 106

Answer 1

The correct option is A 106


$\because$ Spot diameter $=2r{\theta }_a$

here, ${\theta }_a={\sin }^{-1}Na$

$={\sin }^{-1}\sqrt{{1.5}^2-{1.485}^2}$

$={12.216}^{\circ }=0.213\text{rad}$

$D=2\times 1000\times 0.213=427\mu \text{m}$

Total length of photo-detector array
$427+50+50\mu \text{m}=527\mu \text{m}$

Diameter of one photodetector $=5\mu \text{m}$
So, total number of photo detector in array

$=\frac{527}{5}\simeq 106$