# Archives

# Lens

**not**transparent for humans. For certain cameras they are transparent however.

The object points T0 an B0 are mapped to image points T1 and B1 by lens element number 1. The lens elements are numbered starting from object side.

The images T1 and B1 then become the new “object points” of lens element 2 and map T1 and B1 to “images of image” of T0 and T0, called T2 and B2″.

A lens with 10 lens elements accordingly generates sequences

T0->T1->T2->… -> T10

and

B0->B1->B2->….-> B10

It can be smaller or bigger than the object.

Image of microscopic details we of course want to be larger than the details.

# lens equation

With

f = focal length,

g = distance to object (measured from object side principal plane H)

b = distance to image (measured from image side principal plane H’)

The so called “lens equation” reads

## Solving for focal length

## Solving for distance to object

## Solving for distance to Image

## Interpretation of the lens equation

What can be derived from this formula?

- The Image of infinite distant objects is in the focal plane.

When the object moves to infinity (= when g gets infinitely large), then

Say,

- An object that is at double focal length distance on object side is mapped to an image that is in double focal length distance on image side.
- In other words : If we want a 1:1 mapping in distance X from the sensor you have to choose

(but subtract the distance of the principal points from X)

- If the object distance equals the focal length then the image is at infinity.
- The closer an object coming from infinity approaches the focal length, the closer get image distance and focal length. So holds.
- An object in focal length in front of the lens is mapped to infinity on image side.
- For an object closer to the lens than the focal length holds, say, the image is generated on the
**object side**(!) of the lens.

# Lens Types

# lensmaker formula

The formula (at the bottom of this post) shows for thin, spherical lenses the relationship between shape and power.

Be d center thickness of the lens element.

and be the radii of the spheres that describe the surfaces.

Keep the sign conventions for radii in mind, however!

be the index of refraction of the medium outside the lens and

n be the index of refraction of the lens material.

f be the focallength of the lens and

D be it’s Power,

**generally**in the paraxial region:

**Is the surrounding medium air**, we get (because ) the approximation:

**thin**(idealizing ), the formula simplifies to

**Lensmaker’s formula:**

# Light

Light that we can see (“visible light”, “VIS”) is a small part of a spectrum of a thing called “electromagnetic radiation”, distinguished by something we call “wavelength”.

As the wavelength varies in the visible spectrum, the light *appearantly* changes color from violet to red.

There are no actual boundaries between one range of wavelengths and another. So numbers associated with a certain range are only approximate.

If we explore the spectrum from long wavelengths to shorter wavelengths, we meet :

- “radio waves” : regular broadcast wavelengths are for example 500 meters long, but even longer radio waves exist
- “short waves” : (“Radar waves”, “Millimeter waves”)
- “infrared”
- “visible light”
- “ultraviolet light”
- soft x-rays
- x-rays
- hard x-rays
- gamma rays

(C) Wikipedia, file : https://upload.wikimedia.org/wikipedia/commons/c/cf/EM_Spectrum_Properties_edit.svg

# LM

LM A = Load Macro file A

# Lock Ring

Rings of M12x0.5 female thread to fix s-mount lenses using the principle of the counter nut.

Lock-Rings are available from stock at www.lensation.de