# magnification

a) For telecentric lenses this is  the ratio of image size to object size
b) For entocentric lenses this is  the ratio of image size to object size at a given distance.

Example (telecentric lens)
If you want to map an obbject of 10mm diameter to s Sensor with 1/3″ (= 6mm diagonal!), you need a magnification of 6/10 = 0.6x
The lower the magnification, the larger the visible object section. Say, if you can’t get a lens with the desired magnification, you can choose a lens with a slightly smaller magnification, eg 0.55x instead of 0.6x in the above example.
Example (entocentric lens)
With a 1/2 “Sensor (8mm diagonal), a distance of 500mm and an object cutout of 16mm diagonal,   the magnification is  8/16 = 0.5.
Doubling the distance (to 1000mm) allows the lens to see about twice as much (32mm ). As a result, a magnification of 8/32 = 0:25 results.
In particular, the magnification at infinity is zero!
Since for entocentric lenses the FOV changes with the working distance, the magnification changes too!
Each entocentric lens achieves each magnification (if it can be used beyond the MOD)! .. We just have to choose the right distance between the object and the camera.
So there’s the naive hope that just one entocentric lens could be enough for all applications then …
The Problem is however, that (for entocentric lenses) with the distance to the object, also the perspective changes. Telecentric lenses keep the perspective!
Typical high magnifications in image processing end at 10x.
Typical high magnifications in microscope imaging end at 100x, where magnifications above 40x usually need immersion, say, the lens is used in oil!.
When you read about higher magnifications like 200x and higher, there’s an excellent chance that the size of the monitor is also included!

# main optical axis

The Symmetry axis of a lens or a lens system.

# Reflection at a plane in 3D

A flat mirror in 3D is descibed by the direction cosines of a surface normal and a point P on it’s surface.

We construct the image A’ of a point A by these steps

• translate the origin of the coordinate System to the point P
• rotate the coordingate system so, that the z-axis of the coordinate system coincides with the surface normal in P)
• mirror point A in this new coordinate system
• unrotate the coordinate system to it’s old rotation
• untranslate the origin to it’s old position

## Translation of the coordinate system in 3D so that the Origin is in P.

where are the cartesian coordinates of point P=()

Proof that is indeed mapped to :

## Rotation in 3D around the Origin (now in P) so that the z-axis coincides with the surface normal

with

Proof, that each point is mapped to

with

# Reflection at a plane in 3D

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Where

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Missing $inserted. leading text: R = R_  p = (lp_x + mp_y + np_z) =$ length from the origin to point P