Question

A double convex lens is used to couple a laser beam of diameter 5 mm into an optical fiber with a numerical aperture of 0.5. The minimum focal length of the lens that should be used in order to focus the entire beam into the fiber is

• A. $4.33\text{mm}$
• B. $2.50\text{mm}$
• C. $5.00\text{mm}$
• D. $1.44\text{mm}$

Answer 1

The correct option is A $4.33\text{mm}$

N.A. $=\sin {\theta }_a=0.5$
$\therefore {\theta }_0={\sin }^{-1}0.5={30}^{\circ }$
$D=5\text{mm}$



We have to find this distance ${}^{\prime }{X}^{\prime }$, as it is the focal of the lens
$\tan {30}^{\circ }=\frac{D/2}{x}$
$\frac{1}{\sqrt{3}}=\frac{5}{2x}$
$x=\frac{5\sqrt{3}}{2}=4.33\text{mm}$