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In a compound microscope, the total distance between the objective lens and the eyepiece is determined by the focal lengths of the lenses. The focal length of the objective is denoted as f₁ and that of the eyepiece as f₂. The correct formula for the distance between the objective and the eyepiece is indeed the sum of their focal lengths, expressed as d = f₁ + f₂.

When light passes through the objective lens, it converges to a point known as the focal point, and then, as it travels towards the eyepiece, it is further magnified as it passes through the eyepiece. Thus, the effective distance that must be accounted for between the two lenses is the sum of their focal lengths. This arrangement allows for the proper alignment and functioning of the microscope, ensuring that the image is magnified correctly when viewed through the eyepiece.

Understanding this relationship is crucial for designing and using microscopes effectively, as it impacts the overall magnification and clarity of the image produced.