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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