Under what circumstances, if any, will a converging lens form an inverted image of a real object? Under what circumstances, if any, will a diverging lens forms an erect image of a real object?

To understand the circumstances under which a converging lens forms an inverted image of a real object and a diverging lens forms an erect image of a real object, we need to consider the nature of these types of lenses and their focal lengths.

1. Converging lens (convex lens):
A converging lens has a thicker center and causes light rays to converge (come together) after passing through it. It can form both real and virtual images depending on the placement of the object relative to the lens. Specifically, a converging lens will form an inverted image of a real object when the object is placed beyond its focal point.

- If the object is located beyond the focal point of the lens (object distance greater than the focal length), the converging lens will form a real image. This real image will be inverted, meaning that the top of the object will be at the bottom of the image formed.

2. Diverging lens (concave lens):
A diverging lens has a thinner center and causes light rays to diverge (spread out) after passing through it. This type of lens can only form virtual images, which are always erect (upright) and can't be projected onto a screen.

- Regardless of the position of the object, a diverging lens will always form an erect image. This means that even if the object is located close to or far from the lens, the image formed will be upright and smaller than the object.

In summary, a converging lens forms an inverted image of a real object when the object is placed beyond its focal point, while a diverging lens always forms an erect image of a real object regardless of its position relative to the lens.