The Numerical Aperture (NA) (for fiber optics) is usually used to denote the acceptance cone for a multi-mode fiber.
Does NA also describe the expansion of light emitted from the end of a fiber?
I have a 1 mm core 0.22 NA PMMA fiber, I would like to collimate the light once it's reached a 1.5" diameter.
$$
n\sin(\theta)=NA \\
\theta = \arcsin(\frac{.22}{1.4914}) \\
\frac{.5 \cdot 38 [mm]}{ \tan(\theta)}=\left \{ \text{focal length} \right \}
$$
So, I should need a ~130 mm focusing lens?
edited in response to answer below
Is n the index of refraction of the fiber core (1.4914), or free space (1)?
Best Answer
Yes, but.
The quality of the collimated beam may not be fantastic. And it depends on how the light is launched into the fiber. If the incident light has a narrow angular dispersion, and the fiber is short and/or of very good quality with few bends, then the light coming out will have a low angular dispersion. But if the incident light is converging at an angle close to the NA of the fiber, then your analysis should be ok.