Relating Image Distance and Image Height

[swooshfactory]

Regarding the thin lens equation,

1/s + 1/s' = 1/f

where s= distance of object from lens, s' = distance of image from lens, and f=focal length, can h and h' (h = height of object and h' = image height) be substituted from s and s'? I know the values are related through similar triangles, I am just not positive that they can be substituted in this equation. Could anyone shed some light on this being a valid substitution?

 

[Kurdt]

You can't replace image distances with image heights in the thin lens equation but they are related by transverse magnification.

$$M_T = \frac{y_i}{y_0} = -\frac{s_i}{s_0}$$

This occurs because in geometrical optics they both form sides of similar right triangles.

 

[baba89]

Yes, h and h' can be substituted for s and s' in the thin lens equation. This is because the thin lens equation is based on the principles of similar triangles. In a thin lens system, the object and its image are related through similar triangles, where the height of the object and the height of the image are proportional to their respective distances from the lens. Therefore, by substituting h and h' for s and s' in the thin lens equation, we are essentially using the principles of similar triangles to relate the image distance and image height. This substitution is valid and commonly used in calculations involving thin lenses.