An object is placed at a distance of $ 20 ext{ cm}$ in front of a concave mirror and its image is formed at a

Question

An object is placed at a distance of $ 20	ext{ cm}$ in front of a concave mirror and its image is formed at a distance of $ 60	ext{ cm}$ on the same side as the object. The magnification produced by the mirror will be:

Examoogle · Accepted Answer

The correct answer is Option D: 3. The magnification of a spherical mirror is given by the formula $m = -\frac{v}{u}$. Given that the object distance is $u = -20	ext{ cm}$ and the image distance is $v = -60	ext{ cm}$ (since the image is formed on the same side as the object in front of a concave mirror), substituting these values gives $m = -\frac{-60}{-20} = -3$.

Step-by-Step Solution & Concepts:
The magnification of a spherical mirror is given by the formula $m = -\frac{v}{u}$. Given that the object distance is $u = -20	ext{ cm}$ and the image distance is $v = -60	ext{ cm}$ (since the image is formed on the same side as the object in front of a concave mirror), substituting these values gives $m = -\frac{-60}{-20} = -3$.

Working Principle: In sign convention for mirrors, distances measured in the direction of incident light are taken as negative. For a concave mirror, when both the object and real image are on the same side, both $u$ and $v$ are negative. The linear magnification $m$ represents the ratio of the height of the image to the height of the object, which is also equal to $-\frac{v}{u}$.

Key Formulas: $m = -\frac{v}{u}$ — Linear magnification for mirrors in terms of image distance ($v$) and object distance ($u$); $m = \frac{h_i}{h_o}$ — Magnification in terms of image height ($h_i$) and object height ($h_o$)

Key Points: Object distance ($u$) is always negative by convention ($u = -20	ext{ cm}$ here).; When an image is formed on the same side as the object (real image), the image distance $v$ is also negative ($v = -60	ext{ cm}$ here).; A negative magnification value ($-3$) indicates that the image formed is real and inverted, and its size is 3 times larger than the object.; Concave mirrors can produce both real and virtual images depending on the object's position.

Advantages: Provides high magnification for detailed examination of objects; Used in astronomical telescopes, headlights, and shaving/makeup mirrors

Disadvantages: Subject to spherical aberration causing distorted peripheral rays

Applications: Reflecting telescopes; Headlights of vehicles; Entomological and medical examination mirrors

Additional Info: Option D gives $-3$, which correctly accounts for the negative signs of both $v$ and $u$.. Option A ($+3$) is incorrect because it ignores sign conventions leading to a positive sign.. Option B ($-1/3$) and Option C ($+1/3$) confuse mirror magnification formula with lens formula or invert $v$ and $u$ ratio.

Answer: D is correct — The magnification produced by the concave mirror is -3, calculated using the formula $m = -\frac{v}{u}$.

Exam Tip: Always remember the sign difference between lenses and mirrors: for mirrors, magnification is $m = -\frac{v}{u}$, whereas for lenses, magnification is $m = +\frac{v}{u}$.

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