A stamp collector is viewing a stamp with a magnifying glass...

A stamp collector is viewing a stamp with a magnifying glass held next to her eye. Her near point is $25 \mathrm{~cm}$ from her eye. $\quad$ (a) What is the refractive power of a magnifying glass that has an angular magnification of $6.0$ when the image of the stamp is located at the near point? (b) What is the angular magnification when the image of the stamp is $45 \mathrm{~cm}$ from the eye?

Key Concepts

Angular Magnification

Angular magnification is the factor by which the apparent angular size of an object is increased when viewed through an optical instrument compared to the naked eye. It quantifies how much larger the object appears due to the optical aid and is especially relevant in instruments like magnifying glasses, microscopes, and telescopes.

Near Point

The near point is the closest distance at which the human eye can focus an object clearly. For a typical adult, this distance is about 25 centimeters. This parameter is critical in optical calculations, particularly in vision correction and magnification, as it sets a limit on how close an image can appear comfortably to the eye.

Refractive Power

Refractive power, measured in diopters, is defined as the inverse of the focal length of a lens (with the focal length in meters). It describes the lens’s ability to converge or diverge light. In magnifying instruments, a higher refractive power corresponds to a shorter focal length, which can produce a greater angular magnification.

Thin Lens Equation

The thin lens equation relates the object distance, image distance, and focal length of a lens through the formula 1/f = 1/d_o + 1/d_i. This equation is fundamental in geometrical optics for determining image characteristics such as location, size, and type (real or virtual), and is essential in the design and analysis of optical instruments like magnifying glasses.

Virtual Image

A virtual image is formed by diverging rays that appear to originate from a common point behind the lens, although they do not actually converge there. In optical instruments like magnifying glasses, the formation of a virtual image allows the object to appear larger and be observed comfortably by the eye, often positioned at the near point for optimal viewing.

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