A convex lens of power +12 D is used as a magnifier to examine a wildflower. What is the angular

step 1 Angular magnification is given by n over f, but 1 over f is power. Putting the numbers in, we ha

A convex lens of power +12 D is used as a magnifier to...

A convex lens of power $+12 \mathrm{D}$ is used as a magnifier to examine a wildflower. What is the angular magnification if the final image is at (a) infinity or (b) the near point of $25 \mathrm{~cm} ?$

Key Concepts

Angular Magnification

Angular magnification is the measure of how much larger an optical instrument makes an object appear compared to the naked eye. It is calculated as the ratio of the angular size of the image seen through the instrument to the angular size of the object when viewed directly at a standard distance, typically using the near point as a reference for comfortable viewing.

Lens Power and Focal Length

Lens power, usually measured in diopters, is the inverse of the focal length (in meters) and determines how strongly a lens converges or diverges light. In a convex lens, a higher positive power indicates a shorter focal length, which is crucial for determining the object placement for image formation and for the calculation of magnification in optical devices.

Virtual Image Formation

Virtual image formation occurs when the light rays after passing through a lens do not actually converge to form an image, but instead appear to emanate from a location behind the lens. This is important in magnifiers where the object is placed within the focal length, producing an upright, magnified virtual image that the eye can easily focus on.

Near Point (Least Distance of Distinct Vision)

The near point is the minimum distance at which the human eye can focus on an object clearly, typically taken as 25 cm for a normal eye. This distance is used as a reference for calculating angular magnification because it represents the closest distance at which unaided vision can normally resolve detail.

Simple Magnifier

A simple magnifier is an optical instrument that uses a single convex lens to produce an enlarged virtual image of an object. Its functionality relies on placing the object within the focal length of the lens, allowing the observer to view a magnified image either at infinity for relaxed viewing or at the near point to maximize angular magnification.

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