The magnification of object placed 10 cm from a convex mirror of radius of curvature 20 cm will be?

HSSC Staff Nurse - 2015

General Knowledge

Hard

Appeared in: HSSC Staff Nurse - 2015

Explanation

The calculation correctly determines the magnification produced by a convex mirror for a given object distance and radius of curvature.
First, the focal length (f) is calculated from the radius of curvature (R). For a convex mirror, f = R/2 = 20/2 = +10 cm. The sign is positive as the focus is behind the mirror.
The object distance (u) is given as 10 cm. By sign convention, it is -10 cm.
Using the mirror formula 1/f = 1/v + 1/u, the image distance (v) is calculated: 1/10 = 1/v + 1/(-10), which gives v = +5 cm.
Finally, the magnification (m) is calculated using m = -v/u = -(+5)/(-10) = 0.5.
A magnification of 0.5 means the image is half the size of the object, erect, and virtual, which is characteristic of convex mirrors.

Option A: A value of 0.2 is incorrect and would result from an error in calculation, such as misinterpreting the sign convention or the formulas.
Option C: Magnification is 1 only for a plane mirror, or for a concave mirror when the object is placed at the center of curvature (2f). A convex mirror always produces a diminished image (magnification less than 1).
Option D: Infinite magnification is not a physically realistic outcome for this setup. An image is formed at infinity (leading to undefined magnification) only when an object is placed at the focal point of a concave mirror.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of magnification for a convex mirror using the mirror formula as background academic context rather than a clinical decision trigger.
This physics principle is not directly clinical but is fundamental to understanding optics, which is the basis for how vision works and how corrective lenses are prescribed.
Convex mirrors have important safety applications, such as in vehicle side-view mirrors and at blind corners in hallways and roads, because they offer a wider field of view.
The diminished, virtual image allows a driver to see a larger area behind them. This is why these mirrors carry the warning: 'Objects in mirror are closer than they appear'.

How to Approach the Question

Identify the type of optical instrument (convex mirror) and list the given physical quantities: object distance (u = 10 cm) and radius of curvature (R = 20 cm).
Apply the standard Cartesian sign convention: distances measured in the direction of incident light are positive, and those against it are negative. The object is always placed to the left, so u is negative. For a convex mirror, R and f are positive.
Calculate the focal length (f) using the relation f = R/2. Here, f = 20/2 = +10 cm.
Substitute the known values (f and u) into the mirror formula: 1/f = 1/v + 1/u, to find the image distance (v).
Calculate the magnification (m) using the formula m = -v/u.
Interpret the result: a positive magnification indicates a virtual and erect image, while a value less than 1 indicates a diminished image, which is expected for a convex mirror.

Concept Tested & Keywords

Concept Tested: Calculation of magnification for a convex mirror using the mirror formula.
Stem keywords: magnification, convex mirror, radius of curvature, object distance
Lead-in keywords: will be?

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E6 Physiology Guyton 4SAE Part 3 pp. 139-141, 138-140