Question

An object 37.5cm in front of a certain lens is imaged 8.20 cm in front of that lens (on the same side as the object). What typeof lens is this and what is its focal lenght? Is the image real orvirtual?

Answer 1

The lens is a diverging lens with a negative focal length, indicating the image is virtual.

Step-by-step explanation:

The scenario described involves an object being imaged on the same side as the object itself and closer to the lens. This suggests that we are dealing with a diverging lens, as converging lenses produce real images on the opposite side. To determine the focal length and the nature of the image, we can use the lensmaker's equation 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.

Given that do = -37.5 cm (the negative sign indicates the object is on the same side as the incoming light) and di = -8.20 cm (again, negative since the image is on the same side as the object), we can calculate the focal length as follows:

1/f = 1/(-37.5) + 1/(-8.20)

Upon solving, we find the focal length f is negative, confirming the lens is indeed a diverging lens. Additionally, since the image is formed on the same side of the lens as the object, the image is virtual.