Properties of the Lens

1. Camera Lens

blue - Basic Property
red - Symmetry Property
black - Consequent Property

Here are 3 properties (as illustrated above):

1. Basic Property: Parallel rays that enter the thin lens, will intersect at the focus (focal) point
2. Symmetry Property: Non-parallel rays that enter the lens from different angles will become parallel after leaving the thin lens
3. Consequent Property: All rays entering the lens' center, will not undergo any divergence in its path (i.e. continue on in the same straight direction)

3 Key Formulas:

$$\frac{X}{\hat{Z}}=\frac{x}{\hat{z}}\text{and}\frac{Y}{\hat{Z}}=\frac{y}{\hat{z}}$$ $$\frac{1}{\hat{Z}}+\frac{1}{\hat{z}}=\frac{1}{f}$$ $$Zz=f^2$$

2. Depth of Field

Larger Aperature: more light, shallower DoF
Smaller Aperature: less light, depper DoF
Pinhole case: Pinhole aperature, very large DoF

Depth of Field (DoF) is the range of depths that appear acceptably sharp.