An object is placed outside the focus of a diverging lens, as shown below. The image produced is (A) virtual, upright, on the object side of the lens (B) virtual, upright, on the opposite side of the lens from the object (C) virtual, inverted, on the opposite side of the lens from the object (D) real, inverted, on the object side of the lens (E) no image is formed

Diverging lenses are lenses that cause light rays diverging from a point to diverge even more, creating the appearance that the light rays come from a point closer to the lens than they actually do. The most common type of diverging lens is a concave lens. When an object is placed outside the focus of a diverging lens, the image produced is virtual, meaning that it cannot be projected onto a screen. Virtual images are formed on the same side of the lens as the object and are always upright and smaller than the original object.

Now let's analyze each of the given options: (A) virtual, upright, on the object side of the lens - This option matches the properties of images produced by diverging lenses. (B) virtual, upright, on the opposite side of the lens from the object - Diverging lenses create virtual images on the object side of the lens, so this option is incorrect. (C) virtual, inverted, on the opposite side of the lens from the object - Diverging lenses create virtual, upright images, making this option incorrect. (D) real, inverted, on the object side of the lens - Diverging lenses create virtual images, not real images, so this option is incorrect. (E) no image is formed - An image is always formed when an object interacts with a lens, whether the image is real or virtual, so this option is incorrect.

After analyzing each option, we can determine that the correct answer is (A) virtual, upright, on the object side of the lens. This option matches the properties of images produced by diverging lenses when an object is placed outside the focus of the lens.