Question

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

Short answer

The image is always located at a distance of \({{\rm{d}}_{\rm{i}}}\).

Step-by-step solution

Define Image

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.

Explanation

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.