Final answer:
The position of the image for a -6.30 diopters lens held 10.5cm from an object is virtual, meaning it appears on the same side as the object and no real image is formed.
Step-by-step explanation:
The student has a question regarding the image formation by a lens with a known focal length. We're given that a lens with a focal strength of –6.30 diopters (D) is held 10.5cm from an ant that is 1.00mm high. The student has asked for the position of the image formed by the lens.
First, we must understand the relationship between the focal length (f), the object distance (do), and the image distance (di). This relationship is given by the lens formula, which is 1/f = 1/do + 1/di. The focal length for a lens in meters is the inverse of the diopter value, which would be f = -1/6.30 m or approximately -0.159 meters (or -159 mm since the object distance is provided in centimeters).
Using the lens formula and substituting the given values, we get:
1/(-159mm) = 1/(105mm) + 1/di
Solving for di, we find the image distance. Here, we must determine the sign of di to know where the image forms. A negative image distance indicates that the image is virtual and on the same side of the lens as the object. In contrast, a positive image distance implies that the image is real and formed on the opposite side of the lens.
This concept is key to determining whether the image is virtual or real. Based on the negative diopter value of the lens, it indicates a diverging lens, which generally forms virtual images. Therefore, the image formed will be virtual, which means that no real image is formed, and the image appears on the same side of the lens as the object.