Final answer:
The nature of the image formed by a diverging lens placed 40.0 cm to the right of the object with a focal length of -20.0 cm is virtual, and its location is 40.0 cm behind the lens.
Step-by-step explanation:
To determine the nature and location of the image formed by a diverging lens, we can use the lens formula:
1/f = 1/do - 1/di
where f is the focal length, do is the object distance, and di is the image distance.
In this case, the object distance is 40.0 cm, and the focal length is -20.0 cm (given that the lens is diverging, the focal length is negative). Plugging these values into the formula, we have:
1/-20.0 = 1/40.0 - 1/di
Simplifying the equation, we find that the image distance is -40.0 cm. Since the image distance is negative, it means that the image formed is a virtual image. The negative sign indicates that the image is on the same side as the object, but behind the lens. Therefore, the nature of the image is virtual and its location is 40.0 cm behind the lens.