A compound microscope has objective and eyepiece focal...

A compound microscope has objective and eyepiece focal lengths of $5.9 \mathrm{~mm}$ and $1.9 \mathrm{~cm}$, respectively. If the lenses are $9.7 \mathrm{~cm}$ apart, what is the instrument's magnification?

Key Concepts

Compound Microscope

A compound microscope is an optical instrument that uses a combination of two or more lenses—in particular, an objective lens and an eyepiece lens—to produce a magnified image of small objects. The objective lens creates a real, magnified image of the specimen, which is then further magnified by the eyepiece to provide an enlarged virtual image to the viewer.

Focal Length

The focal length of a lens is the distance from the lens at which parallel rays of light either converge to a point (in converging lenses) or appear to diverge from (in diverging lenses). In microscopy, the focal lengths of the objective and eyepiece lenses are crucial parameters that determine the magnification and resolution of the instrument.

Objective Lens Magnification

The magnification produced by the objective lens is determined by its ability to create an enlarged real image of the specimen. This magnification is typically approximated by the ratio of the distance between the lenses (often referred to as the tube length) to the focal length of the objective, emphasizing the role of the objective in setting the initial scale of magnification.

Eyepiece (Angular) Magnification

The eyepiece functions as a simple magnifier that further enlarges the real image produced by the objective lens. Its magnification, also known as angular magnification, is typically calculated by dividing the near point distance of the human eye by the focal length of the eyepiece, thereby determining how much larger the image appears when observed.

Total Magnification

The overall magnification of a compound microscope is the product of the magnifications of the objective and the eyepiece. This total magnification provides a measure of how much larger the final image is compared to the object itself, combining both the enlargement of the objective and the additional angular magnification of the eyepiece.

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