Final answer:
The distance between the objective and eyepiece lenses when the final image is formed at infinity is typically the sum of their focal lengths, often standardized at 16 cm for microscopes.
Step-by-step explanation:
When the final image is formed at infinity in an optical instrument like a microscope or telescope, the distance between the objective lens and the eyepiece lens must be equivalent to the sum of their focal lengths (for a refracting telescope) or the optical tube length (for a microscope).
Typically, for microscopes, this distance, often referred to as the tube length, is standardized to 160 mm (or 16 cm). This ensures that rays that pass through the objective lens focus at the focal point of the eyepiece lens, and then emerge as parallel rays, creating an image at infinity. The objective forms an image at its focal plane, and this image acts as an object for the eyepiece lens which has its object-side focal point coinciding with the image-side focal point of the objective lens.