# Numerical Aperture of thick lens

How to calculate numerical aperture of a thick lens ? Suppose we have a thick biconvex lens whose radius of curvature 24.5 mm, center thickness 9mm , diameter 25.4 mm and focal length 25.4 mm. Then what will be the numerical aperture?

According to the definition of the numerical aperture the lens being a thin or a thick would not contribute a difference to the value of the numerical aperture. Where the numerical aperture of an optical instrument, is a measure for how much light it can accept Wiki, which is given by the following equation $$NA = n \sin(\theta)$$ Where, $$n$$ is the refractive index of the medium through which the lens is placed in, and $$\theta$$ is the acceptance angle which varies as you the object is placed at different distances from the lens.
Assuming, you are placing the object at the focal point, then knowing the diameter of your lens $$D$$ , and the focal length $$f$$ you can find angle $$\theta$$, where $$\theta \approx \tan^{-1}\left( \dfrac{D}{f}\right)$$ Knowing $$\theta$$, you can use the numerical aperture formula to calculate it, if the object is placed at a distance $$d$$ from the lens rather than the focal length, then we simply interchange $$f$$ with $$d$$.