# Image distance for a thin lens

For a thin lens we have:

$$\frac{1}{p}+\frac{1}{q}=\frac{1}{f}$$

Where $p$ is the object distance, $q$ is the image distance and $f$ is the focal point of the lens. Having worked with lenses a little bit, I was wondering how the image distance is defined. I know that for a lens, if you stick a screen anywhere after the lens, you can get some sort of image to appear on it. Is the image distance the distance where the resolution of the image is a maximum, or is there a different way of defining that distance?

The image distance is where the image achieves maximum focus. If the object is a point source of light and the lens is ideal, then the image will be a point at the image distance. Putting a screen at any other distance will create a larger circle, which is a blurry image of the point.

• Interesting. So for a point source the image distance should be the focal point? Also for a non-point source, how would we measure the focus of the image? In an experiment we can look at an image and determine if it is blurry. Is there an equation that gives a measure of focus for an image?
– mphy
Jul 11, 2017 at 17:31
• @mphy In most situations, the image distance will be different than the focal length. In fact, the closer the object distance is to the focal length, the further away the image will be. It is only when the object is at a far distance (much larger than the focal length) that the image is formed near the focal length. Jul 11, 2017 at 21:57
• @mphy The mathematical way of describing how an imaging system blurs an image (and the term to google) is the Point-Spread Function. Jul 11, 2017 at 22:04

Image distance is the distance of the image from the geometric centre or optic centre of the lens on the principal axis, measured along the principal axis.

Similarly, object distance is the distance of the object from the geometric centre or optic centre of the lens on the principal axis, measured along the principal axis.