# What is the proof that we can use virtual object to know the place of formation of image in case of convex/concave lens?

What is the proof that we can use the location of virtual image in the lens formula to get the location of the image (convex/concave lens)? The following problem might make my question more clear. The proof for the case of plane mirror is quite easy using ray diagrams but I'm getting contradictory results when I try to use the same for convex/concave lens.

In this image "p" is the location of virtual object and "r" is the location of the image formed after reflection . I would like to restate my question as to Why can we substitute the distance of "P" in the lens formula to get the location of the image formed after refraction by the arriving rays? What is the proof?

• Typo? Replace virtual image with virtual object in the title Oct 17, 2020 at 7:59
• What is the proof? When the concept of a virtual object is incorporated into the lens/mirror formula the predictions relating to the image are correct. Oct 17, 2020 at 8:01
• In all physics proof is experimentally verifying the prediction to within the limits your model claims to be valid under. I'm not sure if you mean something other than that, but that's what "proof" means to me in physics. Physics is not mathematics in this regard. Even if the math in physics is correct, a model can still be shown to be wrong (or not suited to intended purpose) by experiment. Oct 17, 2020 at 8:15
• "In this image "p" is the location of virtual object and "r" is the location of the image formed after reflection." You mean after refraction. Oct 18, 2020 at 18:19