Optical Image Formation | Sahithyan's Notes

An optical image forms when multiple light rays, originating from the same point, converge at a different point, creating contrast against the background.

The object emits light, or more commonly reflects incident light from another source
Light energy at the image depends on how much light the object reflects and the area of the lens surface

Lens equation

\frac{1}{f} = \frac{1}{u} + \frac{1}{v}

Here:

$f$ : focal distance of the lens
$u$ : distance to the object
$v$ : distance to the image
A lens is a cut-out section of a spherical surface. Its curvature determines $f$ .
For a given $f$ , exactly one point produces a real focused image
Most practical images form between the optical center and the focal length
The quantum of light entering the lens depends on the lens surface area it passes through
Shorter focal lengths require sharper curves, reducing the lens surface area

Depth of field

Depth of field is the distance between the nearest and furthest points in object space that produce a properly focused image in the image plane.

Only one plane in the object region is at proper focus, per the lens equation
Objects nearer or farther than this plane are slightly out of focus
Since the sensor integrates total light, no difference is visible until the circle of confusion exceeds one sensor element
This tolerance is what creates the depth of field that appears to have focus