An object is placed at 30 cm from a convex mirror with a focal... | General Science MCQ

General SciencePrevious Year Paper 2024

An object is placed at 30 cm from a convex mirror with a focal length of 15 cm. Calculate the image distance (v) using the mirror formula.

15 cm

−15 cm

10 cm

−10 cm

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePrevious Year Paper 2024

Option C

10 cm

Quick Summary:

According to the Cartesian sign convention for spherical mirrors, object distance ( $u$ ) is always negative, while the focal length ( $f$ ) of a convex mirror is positive. Substituting $u = -30\text{ cm}$ and $f = +15\text{ cm}$ into the mirror formula yields an image distance ( $v$ ) of $+10\text{ cm}$ . The positive sign indicates that a virtual and erect image is formed behind the convex mirror.

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🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of the rear-view mirror in a vehicle (which is a convex mirror): objects appear closer and smaller behind the mirror's surface, reflecting a positive virtual image distance.

🧠 Memory Mnemonic / Shortcut Aid

Convex = Positive Focus (CPF): Convex mirrors always have a positive focal length ( $+f$ ) and form virtual images behind the mirror ( $+v$ ).

🔢 Key Formulas

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ — Mirror Formula

$m = -\frac{v}{u}$ — Magnification of a spherical mirror

⚙️ Working Principle

The mirror formula relates object distance ( $u$ ), image distance ( $v$ ), and focal length ( $f$ ) as $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ . Convex mirrors are diverging mirrors that always form virtual, erect, and diminished images behind the mirror's pole for real objects.

📌 Key Points

▸
Object distance ( $u$ ) is taken as negative ( $-30\text{ cm}$ ) by convention.
▸
Focal length ( $f$ ) of a convex mirror is always positive ( $+15\text{ cm}$ ).
▸
A positive image distance ( $v = +10\text{ cm}$ ) means the image is formed behind the mirror.

✅ Advantages

▸
Convex mirrors provide a wider field of view compared to plane or concave mirrors.
▸
They always produce an erect image regardless of object position.

❌ Disadvantages / Limitations

▸
Images formed are always diminished, which can give a distorted perception of distance.

🛠️ Applications / Uses

▸
Rear-view mirrors in automobiles to view traffic behind.
▸
Security mirrors in hallways, shops, and ATM machines.

📄 Additional Information

▸
Calculation: $\frac{1}{15} = \frac{1}{v} + \frac{1}{-30} \implies \frac{1}{v} = \frac{1}{15} + \frac{1}{30} = \frac{2 + 1}{30} = \frac{3}{30} = \frac{1}{10} \implies v = +10\text{ cm}$ .
▸
Option B ( $-15\text{ cm}$ ) and Option D ( $-10\text{ cm}$ ) fail to account for the correct sign convention of convex mirrors.

📊 Diagram / Illustration

✅

C is correct — Applying the sign convention ( $u = -30\text{ cm}$ , $f = +15\text{ cm}$ ) to the mirror formula yields $v = +10\text{ cm}$ .

Core Concepts Used

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Mirror Formula Cartesian Sign Convention Convex Mirror Image Formation

💡 EXAM TIP

Always assign signs to known quantities ( $u$ , $v$ , $f$ ) before solving spherical mirror or lens problems; never assign a sign to the unknown quantity being calculated.

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