The distance between the eyepiece and the objective lens in...

The distance between the eyepiece and the objective lens in a certain compound microscope is 20.0 $\mathrm{cm} .$ The focal length of the objective is $0.500 \mathrm{cm},$ and that of the eyepiece is 1.70 $\mathrm{cm} .$ Find the overall magnification of the microscope.

Key Concepts

Eyepiece Lens

The eyepiece lens functions as a magnifying glass for the intermediate image produced by the objective lens, providing angular magnification. Its magnification depends inversely on its focal length, and it enables the viewer to see an enlarged virtual image. The eyepiece is designed to offer a comfortable viewing angle and further increases the overall magnification of the system.

Overall Magnification

The overall magnification of a compound microscope is the product of the magnifications provided by the objective lens and the eyepiece lens. This combined effect allows the microscope to display highly enlarged images of minute objects, making details otherwise unresolvable with the naked eye. The design and focal lengths of both lenses, along with their spatial arrangement, are critical in determining this total magnification.

Objective Lens

The objective lens, positioned closest to the specimen, is responsible for collecting light and forming a real, magnified intermediate image of the object. Its magnification is typically determined by the ratio of the distance from the lens to the intermediate image (often related to the tube length) and its focal length. The short focal length of the objective lens is key to achieving a high initial magnification.

Compound Microscope

A compound microscope is an optical instrument that uses two lenses, the objective and the eyepiece, to produce a magnified image of a small object. The objective lens creates an enlarged real image of the object, which is then further magnified by the eyepiece acting as a simple magnifier. This dual-stage optical system allows for high overall magnification compared to a single lens system.

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