A compound microscope has a barrel whose length is 16.0 cm and an eyepiece whose focal length is

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A compound microscope has a barrel whose length is 16.0 cm...

A compound microscope has a barrel whose length is $16.0 \mathrm{cm}$ and an eyepiece whose focal length is $1.4 \mathrm{cm} .$ The viewer has a near point located $25 \mathrm{cm}$ from his eyes. What focal length must the objective have so that the angular magnification of the microscope will be $-320 ?$

Key Concepts

Tube Length

The tube length, or barrel length, in a compound microscope is the distance between the objective lens and the eyepiece. It is an important parameter in the overall optical design as it affects the intermediate image formation and, consequently, the magnifying power of the microscope. A fixed tube length helps in standardizing the relationship between the objective focal length and the resulting magnification.

Compound Microscope

A compound microscope is an optical instrument that uses a combination of lenses – typically an objective lens and an eyepiece – to produce a magnified image of a small object. Its design relies on positioning the objective close to the specimen to capture detailed information and using the eyepiece to further enlarge the image for observation.

Angular Magnification

Angular magnification refers to the ratio of the angle subtended by the image at the eye to the angle subtended by the object when viewed directly. In the context of optical instruments like microscopes, it indicates how much larger the object appears when observed through the device compared to the naked eye, taking into account the viewing distance or near point.

Objective Lens

The objective lens in a microscope is responsible for collecting light from the specimen and forming a real, magnified image. Its focal length is a critical parameter, as a shorter focal length usually allows for higher magnification. The overall performance of the microscope, including its resolving power and image detail, is highly dependent on the quality and design of the objective lens.

Eyepiece

The eyepiece, or ocular lens, is the lens through which the viewer observes the magnified image produced by the objective. It further magnifies the real image, converting it into a virtual image adjusted for comfortable viewing. Its focal length determines the additional magnification and influences the angular size of the final image as perceived by the observer.

Near Point of the Eye

The near point of the eye is the minimum distance at which the eye can comfortably focus on an object, typically around 25 cm for a normal human eye. This distance is used as a reference in designing optical instruments to ensure that the final virtual image produced is positioned at or near the viewer’s near point, maximizing visual comfort and effective magnification.

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