26.1 Physics of the Eye

Image formation by the eye is adequately described by the thin lens equations:
$P = \frac{1}{d_{o}} + \frac{1}{d_{i}} and \frac{h_{i}}{h_{o}} = - \frac{d_{i}}{d_{o}} = m .$
The eye produces a real image on the retina by adjusting its focal length and power in a process called accommodation.
For close vision, the eye is fully accommodated and has its greatest power, whereas for distant vision, it is totally relaxed and has its smallest power.
The loss of the ability to accommodate with age is called presbyopia, which is corrected by the use of a converging lens to add power for close vision.

26.2 Vision Correction

Nearsightedness, or myopia, is the inability to see distant objects and is corrected with a diverging lens to reduce power.
Farsightedness, or hyperopia, is the inability to see close objects and is corrected with a converging lens to increase power.
In myopia and hyperopia, the corrective lenses produce images at a distance that the person can see clearly—the far point and near point, respectively.

The eye has four types of light receptors—rods and three types of color-sensitive cones.
The rods are good for night vision, peripheral vision, and motion changes, while the cones are responsible for central vision and color.
We perceive many hues, from light having mixtures of wavelengths.
A simplified theory of color vision states that there are three primary colors, which correspond to the three types of cones, and that various combinations of the primary colors produce all the hues.
The true color of an object is related to its relative absorption of various wavelengths of light. The color of a light source is related to the wavelengths it produces.
Color constancy is the ability of the eye-brain system to discern the true color of an object illuminated by various light sources.
The retinex theory of color vision explains color constancy by postulating the existence of three retinexes or image systems, associated with the three types of cones that are compared to obtain sophisticated information.

The microscope is a multiple-element system having more than a single lens or mirror.
Many optical devices contain more than a single lens or mirror. These are analysed by considering each element sequentially. The image formed by the first is the object for the second, and so on. The same ray tracing and thin lens techniques apply to each lens element.
The overall magnification of a multiple-element system is the product of the magnifications of its individual elements. For a two-element system with an objective and an eyepiece, this is
$m = m_{o} m_{e},$
where $m_{o}$ is the magnification of the objective and $m_{e}$ is the magnification of the eyepiece, such as for a microscope.
Microscopes are instruments for allowing us to see detail we would not be able to see with the unaided eye and consist of a range of components.
The eyepiece and objective contribute to the magnification. The numerical aperture $(NA)$ of an objective is given by
$NA = n sin α$
where $n$ is the refractive index and $α$ the angle of acceptance.
Immersion techniques are often used to improve the light gathering ability of microscopes. The specimen is illuminated by transmitted, scattered or reflected light though a condenser.
The $f /#$ describes the light gathering ability of a lens. It is given by
$f /# = \frac{f}{D} \approx \frac{1}{2 NA} .$

Simple telescopes can be made with two lenses. They are used for viewing objects at large distances and utilize the entire range of the electromagnetic spectrum.
The angular magnification M for a telescope is given by
$M = \frac{θ'}{θ} = - \frac{f_{o}}{f_{e}},$
where $θ$ is the angle subtended by an object viewed by the unaided eye, $θ'$ is the angle subtended by a magnified image, and $f_{o}$ and $f_{e}$ are the focal lengths of the objective and the eyepiece.

Aberrations or image distortions can arise due to the finite thickness of optical instruments, imperfections in the optical components, and limitations on the ways in which the components are used.
The means for correcting aberrations range from better components to computational techniques.