Callum is examining a stamp that is 3.00 cm square in size with a magnifying glass of refractiv

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Callum is examining a stamp that is 3.00 cm square in size...

Callum is examining a stamp that is $3.00 \mathrm{~cm}$ square in size with a magnifying glass of refractive power $+40.0$ D. The magnifier forms an image of the stamp at a distance of $25.0 \mathrm{~cm}$. Assume that Callum's eye is close to the magnifying glass. (a) What is the distance between the stamp and the magnifier? (b) What is the angular magnification? (c) How large is the image formed by the magnifier?

Key Concepts

Near Point of the Eye

The near point of the eye is the closest distance at which the eye can comfortably focus on an object, typically around 25.0 cm for a normal human eye. In optical devices, the near point is used as a reference distance for calculating angular magnification, ensuring that the magnified image is formed at a location where the eye can comfortably view it.

Image Formation with a Magnifying Glass

A magnifying glass is a converging lens used to form a virtual, enlarged image of an object when it is placed within the focal length of the lens. In this setup, the eye perceives the object under a greater angular size than the object’s actual size, thereby allowing for enhanced detail recognition.

Angular Magnification

Angular magnification describes the ratio of the angle subtended by the image when viewed through an optical device to the angle subtended by the object when viewed with the unaided eye at the near point. It is a crucial concept in understanding how devices like magnifying glasses enlarge the appearance of objects by increasing their perceived size, aiding in tasks that require detailed observation.

Thin Lens Equation

The thin lens equation, 1/f = 1/s + 1/s', is a fundamental relation in geometrical optics that connects the focal length of a lens with the object distance and image distance. This relation is used to determine how a lens forms an image of an object, whether that image is real or virtual, and where it is located relative to the lens.

Refractive Power and Focal Length

Refractive power, measured in diopters, is the reciprocal of the focal length (in meters) of a lens. This concept allows one to easily relate the ability of a lens to converge or diverge light with its focal length. A higher diopter value indicates a shorter focal length, meaning the lens bends light more strongly.