# In this situation, is an endless sequence of images (theoretically) formed?

I was dealing with an optics problem, where an object is placed at $$u= -60$$ cm in front of a biconvex lens of radius of curvature $$R=30$$ cm and refractive index $$\mu=1.5$$ . Simple calculations show that an image (real and inverted) is formed at $$v=60$$ cm .

This isn't what bothers me.

The curved surface of the lens facing the object also acts as a convex mirror of focal length $$f=15$$ cm, and produces a virtual, erect image of the object at $$v_1=10$$ cm.

If this virtual image (let's call it $$I_1$$) were to act as a virtual object at $$u_2=10$$ cm for the lens, it would produce another virtual image ($$I_2$$) at $$v_2=7.5$$ cm.

This process could go on, with each virtual image at $$v_n$$ acting as a virtual object at $$u_{n+1}$$ for the lens to give another image at $$v_{n+1}$$.

Also, each of the images formed by the lens could act as an object for the reflecting surface of the lens which acts as a convex mirror.

So that would mean an infinite string of images (in theory), of lessening brightness, yes, but images nonetheless.

## My question

Does this unending formation of images actually take place?

Or am I wrong in my assumptions somewhere?

If I am, I'd like to stand corrected.