# Image distance

Figure 1: Sketch of an image with a lens. If the object to be imaged is closer than the infinite distance, then the image distance of a real image is greater than the focal length.

The image distance describes the distance between the image generated by an optical lens or a mirror and the image-side main plane along the optical axis . In the case of individual thin lenses, the main plane can be approximated through the lens center.

A real image has a positive image distance, with lenses the object and image are on the opposite sides of the optical axis. In contrast, a virtual image appears to be on the side of the object. The image distance is negative in this case.

The following applies to a converging lens: If the object distance is smaller than , the image distance is negative and a virtual image is created , like a magnifying glass . If it is smaller and larger , there is an increase . If the object distance is just the same , the image size is the same as the object size . If it is larger than then a reduction occurs. ${\ displaystyle g}$${\ displaystyle f}$${\ displaystyle b}$${\ displaystyle 2f}$${\ displaystyle f}$${\ displaystyle 2f}$${\ displaystyle B}$${\ displaystyle G}$${\ displaystyle 2f}$

Diverging lenses create a reduced virtual image of every object. The image is therefore on the object side as seen from the viewer, and the image distance is negative.

## Formulas

The object and image distance are connected by the lens equation :

${\ displaystyle {\ frac {1} {f}} = {\ frac {1} {b}} + {\ frac {1} {g}}}$

Here, the focal length of the lens (the mirror), it is positive for converging lenses, negative for diverging lenses. ${\ displaystyle f}$

The image scale , i.e. the ratio of the image to the object size, is equal to the ratio of the image width to the object width: ${\ displaystyle B / G}$

${\ displaystyle {\ frac {B} {G}} = {\ frac {b} {g}}}$

Note that here positive values ​​of the magnification mean an inverted image (as in Fig. 1), negative values ​​mean an upright image.

## Overview of collective lenses ${\ displaystyle (f> 0)}$

No. Object distance
g
Image distance
b
Image properties
1. g> 2f f <b <2f real, vice versa, scaled down
2. g = 2f 2f = b real, vice versa, same size
3. f <g <2f b> 2f real, reversed, enlarged
4th g = f - Image in infinity
5. g <f - virtual, upright, enlarged