An anatomist is viewing heart muscle cells with a microscope...

An anatomist is viewing heart muscle cells with a microscope that has two selectable objectives with refracting powers of 100 and 300 diopters. When she uses the 100 diopter objective, the image of a cell subtends an angle of $3 \times 10^{-3}$ rad with the eye. What angle is subtended when she uses the 300 -diopter objective?

Key Concepts

Diopter-Focal Length Relationship

Diopters are a measure of a lens's refractive power and are defined as the inverse of its focal length in meters. This means that a higher diopter value corresponds to a shorter focal length, which can result in a higher magnification when imaging, as the lens forms an image with a larger angular size.

Angular Magnification

Angular magnification refers to the increase in the apparent size of an object as viewed through an optical instrument. It is the ratio of the angle subtended by the image at the eye to the angle subtended by the object when viewed with the naked eye. In microscopes, higher angular magnification makes the intricate details of small objects, like cells, more observable.

Microscope Objectives

Microscope objectives are the primary lenses in a microscope system that directly gather light from the specimen and form an image. Different objective lenses with varying diopter ratings change the magnification and resolution of the image. A higher diopter objective decreases the focal length and generally increases the angular size of the cell image, enhancing the details observed.

Angular Subtense

Angular subtense is the angle that an object or image occupies in the observer’s field of view. In microscopy, the angular subtense of the image on the observer’s eye increases with the use of objectives with stronger refracting power, providing a larger, more detailed view of the specimen. This concept is crucial in determining how minute changes in the optical setup can impact image perception.

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