The word lens is from the Latin, shaped like a lentil seed. This is a disk that bulges out of both sides, we call this lens shape, convex – convex. A single transparent convex – convex lens will do the deed. We task the camera lens to gather image forming light rays from a 3 dimensional world (object at different distances) and project their image on a flat light sensitive surface. We task the enlarger lens to gather image forming rays from a flat object (negative / slide) and project that image on a flat light sensitive surface. The two tasks are similar but the differences are profound.
The lens maker’s desire is a lens that projects a faithful image. This has never been achieved. Every lens ever made fails to yield a faithful image because the lens is a wave guide that alters the path of light waves. Our camera and enlarger lenses are converging lenses. Light rays transverse the lens and their paths altered. The light rays emerge, tracing out a cone of light. Sorry to report that some of these redirected rays fail to hit their intended target. These errors are called aberrations from the Latin for deviation.
There are seven major lens aberrations. Five are independent of the color of the light, two are based on the color of image forming rays.
- Spherical Aberration – Differences in focal length center of lens vs. edge of the lens.
- Coma – Circular objects image with a dim tail like a comet,
- Astigmatism - Horizontal rays vs, vertical rays have a different focal length.
- Distortion – A square object images with a barrel or pincushion shape.
- Curvature of field – The project image is not flat, best to project on a curved surface.
- Chromatic Aberration – Longitudinal – The location of the image is a function of its color.
- Chromatic Aberration – Transvers – Focal length of each color different.
The lens maker strives to mitigate these seven aberrations. He/she dealing is using different shape lens elements and a mix of different density glass. The camera lens tasked to image a curved world on a flat, and the enlarger lens tasked to work flat to flat pose different problems.
Some lens elements are cemented together, some are air-spaced. The air-space between the glass is also lens-like in its shape. The air-spaces act just like a glass lens element as their width becomes part of the lens formula. The focal length is the distance from rear nodal to the image when the lens is imaging an object at infinity. The back-focus is the distance lens to image plane. Many times, the camera lens must have a longer back-focus to accommodate mechanical considerations. The rear nodal is thus shifted back towards the camera body. It likely will fall in air behind the lens. Conversely, to make a telephoto less unwieldy, the barrel is artificially shortened by shifting the rear nodal forward. It can even fall in air ahead of the lens. These shifts in the rear nodal are valued art of the lens maker.
Miniature cameras have fixed distances from the flange of the lens mount to the focal plane. Often in the optical path are reflex mirrors and gadgets to measure light. The back-focus distance of a lens must be adjusted so that when the lens barrel is imaging an object at infinity, the apex of the cone of image forming light just kisses the surface of film or sensor. The large format cameras utilize bellows that allow positioning the lens near or far from the film plane. No need to shift the rear nodal, a simple three element of the Tessar generally exceeds what film need to be pictorially useful.