The formula to calculate the aperture area (A) is:
\[ A = \pi \left(\frac{D}{2}\right)^2 = \pi \left(\frac{n}{2f}\right)^2 \]
Where:
Let's say the aperture diameter (D) is 50 mm, the focal length (n) is 100 mm, and the f-number (f) is 2. Using the formula:
\[ A = \pi \left(\frac{50}{2}\right)^2 = \pi \left(\frac{100}{2 \times 2}\right)^2 \]
We get:
\[ A = \pi \times 625 = 1963.50 \, \text{mm}^2 \]
So, the aperture area is approximately 1963.50 mm².
Definition: The numerical aperture (NA) of a lens or optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light.
Formula: \( \text{NA} = n \sin(\theta) \)
Example: \( \text{NA} = 1.5 \sin(30^\circ) \)
Definition: The aperture of a lens is the opening through which light enters the camera.
Formula: \( A = \frac{f}{N} \)
Example: \( A = \frac{50}{2.8} \)
Definition: Numerical aperture is measured to determine the light-gathering ability of an optical system.
Formula: \( \text{NA} = n \sin(\theta) \)
Example: \( \text{NA} = 1.33 \sin(45^\circ) \)
