When an object is placed at a distance of 25 cm from a mirror, the magnification is m1. But the

step 1 In discussion we have a mirror of magnification am. When an object placed front of this mirror a

When an object is placed at a distance of 25 cm from a...

When an object is placed at a distance of $25 \mathrm{~cm}$ from a mirror, the magnification is $m_{1}$. But the magnification becomes $m_{2}$, when the object is moved $15 \mathrm{~cm}$ farther away with respect to the earlier position. If $\frac{m_{1}}{m_{2}}=4$, then find the focal length of the mirror and what type of mirror it is? (a) $20 \mathrm{~cm}$, convex (b) $20 \mathrm{~cm}$, concave (c) $10 \mathrm{~cm}$, convex (d) $10 \mathrm{~cm}$, concave

When an object is placed at a distance of $25 \mathrm{~cm}$ from a mirror, the magnification is $m_{1}$. But the magnification becomes $m_{2}$, when the object is moved $15 \mathrm{~cm}$ farther
away with respect to the earlier position. If $\frac{m_{1}}{m_{2}}=4$, then find the focal length of the mirror and what type of mirror it is?
(a) $20 \mathrm{~cm}$, convex
(b) $20 \mathrm{~cm}$, concave
(c) $10 \mathrm{~cm}$, convex
(d) $10 \mathrm{~cm}$, concave

Key Concepts

Mirror Equation

This fundamental formula for spherical mirrors relates the object distance (u), the image distance (v), and the focal length (f) by the equation 1/f = 1/u + 1/v. It serves as a core tool in analyzing image formation in mirrors and is applicable to both concave and convex types when combined with appropriate sign conventions.

Magnification

Magnification in mirror systems is defined as m = -v/u, where v is the image distance and u is the object distance. Magnification not only tells us the size of the image compared to the object but also, through its sign, indicates whether the image is inverted or upright. This concept is essential when comparing changes in image sizes due to changes in object position.

Sign Conventions in Mirror Systems

Sign conventions provide a systematic way to assign positive or negative values to distances and focal lengths in mirror problems. For instance, in the case of mirrors, the object distance is usually taken as positive, while the image distance and focal length may be positive or negative depending on whether the mirror is concave or convex, which directly impacts the type and properties of the image formed.

Relating Object Position, Image Distance, and Magnification Ratios

When dealing with changes in object position and resulting changes in magnification, the interplay between object distance, image distance, and magnification provides a means to determine the mirror’s focal length. By comparing ratios of magnifications under different conditions, one can establish equations that ultimately lead to finding the focal length and identifying the mirror type (concave or convex) based on whether a real or virtual image is produced.

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