Consider the following statements about a microscope and a telescope : 1. Both the eyepiece and the objective of a microscope are convex lenses. 2. The focal length of the objective of a telescope is larger than the focal length of its eyepiece 3. The magnification of a telescope increases with the increase in focal length of its objective. Which of the statements given above are correct?

A compound microscope utilizes two convex lenses: the objective lens, which creates a real, inverted, and magnified image, and the eyepiece, which further magnifies this image for the observer. In an astronomical telescope, the objective lens has a long focal length compared to the eyepiece to capture more light and provide initial magnification. The magnification (M) of a telescope is mathematically defined as the ratio of the focal length of the objective (fo) to the focal length of the eyepiece (fe), expressed as M = fo / fe. Consequently, increasing the focal length of the objective lens directly increases the telescope's magnifying power. Therefore, statement 1 (both lenses are convex), statement 2 (objective focal length is larger than eyepiece), and statement 3 (magnification increases with objective focal length) are all scientifically accurate.