from: Systematic design of microscope objectives

The vertical dotted line where rays cross at right end of tube length is called the objective's

To the extent that it is, a finite objective's correction is designed for that tube length,

keeping in mind than many objectives also depend on both slide cover glass and eyepiece for correction.

"tube length" is approximately the objective's focal length for its specified magnification,

if that objective was a simple convex lens.

The lower diagram, which is nominally about more modern microscopes,

is arguably also more accurate for some "finite" microscopes,

if

`Objective`

+ `Infinity space`

+ `Tube lens`

are considered together as a compensated "finite" objective.While infinity objectives can be used with a tube lens of any focal length,

specified magnification depends on that focal length.

they do not prevent other photons from also stimulating sensors.

When viewing a three-dimensional scene, perhaps focusing on a near object,

photons scattered from more distant objects may also land on the same photosensors.

Some non-image-forming light can be blocked by an iris diaphragm, as in this diagram:

then provide miserable, incomplete and wrong instructions.

Fortunately, Wikipedia does all right;

`1/f = 1/do + 1/di`

{1} `di`

`f`

`do`

`m = di/do`

{2} `f = (d2 - d1)/(m2 - m1)`

; {3} `d2 = d1 + f*(m2 - m1)`

`m2 = m1 + (d2 - d1)/f`

`m = (L/fo)*(D/fe)`

,...

`m`

= magnification
`L`

= tube length (160mm)
`D`

= normal vision relaxed distance (250mm)
`f`

= focal length
`fo`

= objective focal length
`fe`

= eyepiece focal length
`di`

= lens to image distance
`do`

= lens to object distance
For 160mm tube length, a 10x objective has 16mm focal length

and a 10x eyepiece has 25mm focal length.

For infinity scopes, substitute "tube lens focal length" for "tube length".

Olympus infinity objectives expect 180mm tube lens focal length;

Nikon finite CF BD and M Plan objectives expect 210mm tube length.

`m * lens aperture`

`(m+1) * lens aperture`

`x * lens aperture`

`m / (2 * N.A.)`

`f=1/(2*N.A.)`

is not a bad approximation.`f=1/(2*N.A.) * M/(M+1)`

, where `M`

is rated magnification.
`N.A. = 1/(2 * f/#)`

f/# | 1.2 | 1.4 | 1.8 | 2 | 2.8 | 4 | 5.6 | 8 | 11 | 16 |

N.A. | .4167 | .357 | .417 | .25 | .1786 | .125 | .0893 | .0625 | .045 | .03125 |

Abbe flaws begin to bother above N.A. 0.6-7; elevate an Abbe to optimize filling the objective's back lens.

`DoF2 = DoF1 * (f/#2/f/#1) * (m1/m2)**2`

`diopter = 2 for 500mm fl`

`m = sensor width / frame width`

`0.0022*(((m+1)*f/#)/m)**2`

`0.00055/(N.A.**2)`