Final answer:
The magnifying power of a compound microscope is the product of the magnification by the objective lens and the eyepiece. Linear magnification is calculated using the thin-lens equation for the objective, and angular magnification is calculated for the eyepiece, considering the least distance of distinct vision.
Step-by-step explanation:
To determine the magnifying power of a compound microscope when the final image is formed at the least distance of distinct vision, we have to consider the two stages of magnification. First, the objective lens creates an enlarged real image, and then the eyepiece acts as a magnifying glass to further enlarge this image to produce a virtual image at the least distance of distinct vision, which is typically around 25 cm for a relaxed eye.
The magnifying power of the compound microscope is the product of the linear magnification (mobj) of the objective lens and the angular magnification (Meye) of the eyepiece. The linear magnification of the objective is derived from the thin-lens equation and is defined as mobj = -diobj/doobj, where diobj is the image distance for the objective lens and doobj is the object distance for the objective lens. With the final image at the least distance of distinct vision, the magnification of the eyepiece Meye can be calculated using Meye = 1 + (D/fe), where fe is the focal length of the eyepiece and D is the least distance of distinct vision (25 cm).
The total magnifying power (M) is thus M = mobj × Meye. This total magnification tells us how much larger the final image is compared to the original object when viewed through the microscope.