The distance between the lenses in a compound microscope is 18 cm . The focal length of the obje

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The distance between the lenses in a compound microscope is...

The distance between the lenses in a compound microscope is $18 \mathrm{cm} .$ The focal length of the objective is $1.5 \mathrm{cm} .$ If the microscope is to provide an angular magnification of -83 when used by a person with a normal near point $(25 \mathrm{cm}$ from the eye), what must be the focal length of the eyepiece?

Key Concepts

Near Point

The near point is the closest distance at which the human eye can see an object clearly without strain, typically taken as 25 centimeters for a normal eye. This concept is important in optical design, particularly for devices like microscopes and magnifiers, as it influences the calculation of angular magnification and the perceived clarity of the final image.

Focal Length

The focal length of a lens is the distance from the lens at which parallel rays of light converge to a point (or appear to diverge from in the case of virtual images). In microscopes, the focal lengths of both the objective and eyepiece are crucial parameters that determine the magnifying power and the quality of the image formed.

Angular Magnification

Angular magnification refers to the ratio by which an optical instrument increases the angle at which the image of an object is seen compared to the naked eye. In microscopes, it is the combined effect of the objective and eyepiece lenses that results in a significantly larger apparent size of the object, enhancing the observer's ability to see fine details.

Objective Lens

The objective lens is the first lens in the optical path of a compound microscope, positioned close to the specimen. Its main function is to collect light and form a real, magnified image of the object. The magnification provided by the objective is largely determined by its focal length and its distance from the specimen.

Compound Microscope

A compound microscope is an optical instrument that uses two or more lenses to magnify small objects. It consists primarily of an objective lens, which produces a real, magnified image of the specimen, and an eyepiece lens, which further magnifies that image to yield the final enlarged view perceived by the observer.

Eyepiece Lens

The eyepiece lens functions as a simple magnifier in a compound microscope, taking the real image formed by the objective and enlarging it further for the viewer. Its effectiveness is influenced by its focal length, which determines the angular magnification, making the final image appear larger to the human eye.

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