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