At what distance is an image always located—at \({{\rm{d}}_{\rm{o}}}\) , \({{\rm{d}}_{\rm{i}}}\) , or \({\rm{f}}\) ?

The point where light rays from an object meet, or appear to meet after reflection or refraction, is sometimes referred to as the image. In this concept, a "object" might be anything that light rays are emanating from.

The image is always formed at a distance of\({{\rm{d}}_{\rm{i}}}\)from where the lens or the mirror, can be determined from the lens maker's equation or the mirror's equation which is:

\(\frac{{\rm{1}}}{{{{\rm{d}}_{\rm{i}}}}}{\rm{ = }}\frac{{\rm{1}}}{{\rm{f}}}{\rm{ - }}\frac{{\rm{1}}}{{{{\rm{d}}_{\rm{o}}}}}\)

The value of\({\rm{f}}\)is the focal length of the lens/mirror.

The value of\({{\rm{d}}_{\rm{i}}}\)is the distance between the image and the optical instrument.

The value of\({{\rm{d}}_{\rm{o}}}\)is the distance between the object and the optical instrument.

In some special case, the value of the distance denoted as\({{\rm{d}}_{\rm{i}}}\)may be equal to the focal length denoted as\({\rm{f}}\)"which is the case for objects that are placed at infinity for example" or the distance between the optical instrument and the object\({{\rm{d}}_{\rm{o}}}\)"which is the case for the plane mirror".

Therefore, At the distance \({{\rm{d}}_{\rm{i}}}\), the image is always created.