A concave mirror of focal length 10cm is placed at a distance of 35 cm from a wall. How far from the

A concave mirror of focal length 10cm is placed at a distance of 35 cm from a wall. How far from the wall should an object be placed to get its
image on the wall?
(a) 14 cm (b) 7.78 cm
(c) 21cm (d) 10 cm
*🪞 Concave Mirror & Image Formation - Conceptual Understanding 🪞*
Understanding how a *concave mirror* forms an image is essential for *NEET* and *JEE* aspirants. This problem explores the fundamental properties of concave mirrors and how they create *real images* on a **wall**.
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*🔍 How Concave Mirrors Form Images?*
A *concave mirror* is a **converging mirror**, meaning it brings light rays together to form an image. The nature of the image depends on where the object is placed:
✔ *Beyond the focal point:* The image is **real, inverted, and can be projected on a screen or wall**.
✔ *At the focal point:* The reflected rays become parallel, and the image is formed at **infinity**.
✔ *Inside the focal point:* The mirror produces a *virtual, erect, and magnified* image that cannot be projected.
In this problem, we are given that the **image is formed on the wall**, meaning the image is **real and inverted**. This situation occurs when the object is positioned **at a specific distance beyond the focal point**.
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*📌 Why Does the Image Appear on the Wall?*
For an image to be projected onto a *wall**, it must be **real**. Concave mirrors create real images when parallel light rays converge after reflection. These images can be **captured on a screen* and are always **inverted**.
✔ *The image distance depends on the position of the object.* If the object is placed correctly, the image forms at the given **wall distance**.
✔ **Concave mirrors follow the principles of reflection**, where the angle of incidence equals the angle of reflection, ensuring that the image follows a predictable path.
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*🔎 Key Theoretical Concepts for NEET & JEE:*
1️⃣ *Nature of Image:* The image must be *real and inverted* since it forms on a wall.
2️⃣ *Concave Mirrors Form Real Images:* This only happens when the object is placed beyond the focal point.
3️⃣ *Image Distance & Object Distance Relationship:* The position of the object determines where the image appears.
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*💡 Understanding Real-Life Applications*
Concave mirrors are widely used in various fields due to their ability to form **real images**:
✔ *Headlights & Reflectors:* Concave mirrors focus light to create powerful beams.
✔ *Solar Concentrators:* They focus sunlight to generate energy efficiently.
✔ *Shaving & Makeup Mirrors:* When used up close, they create *magnified virtual images* for better visibility.
In this problem, the *concave mirror acts like a projector**, forming a real image on the **wall* at a specific position.
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*📚 Important Concepts for Competitive Exams*
✔ *Difference Between Real & Virtual Images*
✔ *Reflection of Light & Mirror Laws*
✔ *Applications of Concave Mirrors*
✔ *Concept of Focal Length & Image Distance*
Understanding these principles will *strengthen your problem-solving skills* for JEE & NEET.
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*🎯 Answer:*
Based on theoretical concepts, the correct object position to form an image on the wall is:
✅ *(c) 21 cm*
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