An engraver uses a magnifying glass (f=9.50 cm) to examine some work, as in Figure 26.39 b . The

step 1 Solving part of this problem, from the lens equation I can write 1 by f is equal to 1 by D0 plus

An engraver uses a magnifying glass (f=9.50 cm) to examine...

An engraver uses a magnifying glass $(f=9.50 \mathrm{cm})$ to examine some work, as in Figure $26.39 b .$ The image he sees is located $25.0 \mathrm{cm}$ from his eye, which is his near point. (a) What is the distance between the work and the magnifying glass? (b) What is the angular magnification of the magnifying glass?

Key Concepts

Thin Lens Equation

The thin lens equation relates the object distance (d?), image distance (d?), and the focal length (f) of a lens using the relationship 1/f = 1/d? + 1/d?. This fundamental principle in optics is used to predict where an image will be formed for a given object position and is essential in solving problems involving lenses, such as determining object distances when a virtual image is formed.

Angular Magnification

Angular magnification is defined as the ratio of the angle subtended by the image when viewed through an optical instrument to the angle subtended by the object when viewed with the unaided eye at the standard viewing distance (usually the near point). This concept explains why objects appear larger when viewed through a magnifying glass, even though the physical size of the image does not change.

Virtual Image Formation

A virtual image is an image that cannot be projected on a screen because the light rays do not actually converge at the image point; rather, they appear to diverge from it. In the context of a magnifying glass, a virtual image is formed on the same side of the lens as the object and is essential for creating the enlarged view seen by the eye while keeping the object at a comfortable viewing distance.

Near Point

The near point is the closest distance at which the human eye can comfortably focus on an object. It is typically around 25 centimeters for a normal eye. In problems involving magnifying glasses, the near point serves as the standard reference distance for calculating angular magnification, since the perceived size of an object is compared to its size when it is observed at the near point without aid.

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