A beetle 4.93 mm long is examined with a simple magnifier of...

A beetle 4.93 $\mathrm{mm}$ long is examined with a simple magnifier of
focal length $f=10.1 \mathrm{cm} .$ If the observer's eye is relaxed while
using the magnifier, and has a near-point distance of 26.0 $\mathrm{cm},$
what is the apparent length of the beetle?

Key Concepts

Near-Point Distance

Near-point distance is the closest distance at which the human eye can comfortably focus on an object, typically around 25 to 26 centimeters for a relaxed eye. This distance is used as a reference in optical instruments to determine the maximum useful angular magnification, ensuring that the virtual image formed is at a position where the eye can see it clearly without strain.

Simple Magnifier

A simple magnifier is an optical instrument that consists of a single converging lens and is used to enlarge the appearance of objects. When an object is placed within the focal length of the lens, the resulting virtual image is magnified, allowing for a detailed inspection of small items.

Virtual Image Formation

Virtual image formation is the process by which a lens produces an image that cannot be projected onto a screen because the outgoing rays only appear to be diverging from a common point. In magnifying devices, when the object is positioned within the focal length of the lens, a virtual, upright, and enlarged image is produced, which is essential for magnification as observed by the eye.

Angular Magnification

Angular magnification refers to the factor by which an optical device, such as a magnifying glass, increases the angular size of an object as seen by the observer. This concept is crucial in understanding how the perceived size of an object is enhanced, even though its actual size remains constant, by allowing the eye to observe a larger angle than it would without the device.

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