Solved Light and Geometric Optics CONCAVE MIRRORS Extra | Chegg.com - Free Printable

It looks like you've uploaded a diagram related to geometric optics, specifically involving concave mirrors and object positions. The image shows three different scenarios (labeled 4, 5, and 6) with an object placed at various locations in front of a concave mirror. Each setup includes:

- PA: Principal Axis
- C: Center of Curvature
- F: Focal Point
- V: Vertex (apex) of the mirror
- A blue arrow representing the object (upright or inverted)

We are to analyze the nature of the image formed in each case using ray diagrams and principles of geometric optics for concave mirrors.

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🔍 General Rules for Concave Mirrors:

1. Object beyond C: Real, inverted, diminished image between C and F.
2. Object at C: Real, inverted, same size image at C.
3. Object between C and F: Real, inverted, magnified image beyond C.
4. Object at F: Image at infinity (no image formed).
5. Object between F and V: Virtual, upright, magnified image behind the mirror.

Let’s analyze each case:

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✔ Case (4)

- Object is at point C (center of curvature).
- Object is upright (blue arrow pointing up).
- Position: At C

#### 🔎 Image Characteristics:
- Image will be formed at C (same location as object).
- Image is real, inverted, and same size as object.
- This is because rays from the object reflect such that they converge at C.

> ✔ Image: Real, Inverted, Same Size, Located at C

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✔ Case (5)

- Object is at F (focal point).
- Object is upright.
- Position: At F

#### 🔎 Image Characteristics:
- Rays parallel to the principal axis pass through F after reflection.
- But if the object is at F, rays from the top of the object go toward the mirror and reflect parallel to the axis.
- These reflected rays never converge — they appear to come from infinity.
- So, no real image is formed; the image is at infinity.

> ⚠️ Image: No image formed (image at infinity)

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✔ Case (6)

- Object is between F and V (i.e., within focal length).
- Object is inverted (blue arrow pointing down), but this likely just indicates direction — we assume it's a real object, so inversion may be due to drawing convention.
- Actually, objects are usually drawn upright unless specified otherwise. However, here the arrow points down, which could imply the object is inverted, but in standard optics problems, we consider upright objects unless stated.

But let’s interpret: If the arrow is pointing down, it might mean the object is below the principal axis, but still, the position matters more than orientation.

But regardless, the key is the position: object is between F and V → within focal length.

#### 🔎 Image Characteristics:
- When object is inside F, image is:
- Virtual
- Upright
- Magnified
- Located behind the mirror

This is how magnifying mirrors work (e.g., makeup mirrors).

> ✔ Image: Virtual, Upright, Magnified, Behind Mirror

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📌 Summary Table:

| Case | Object Position | Image Type | Orientation | Size | Location |
|------|------------------------|----------------|-------------|------------|----------------------------|
| (4) | At C | Real | Inverted | Same size | At C |
| (5) | At F | No image | N/A | N/A | At infinity |
| (6) | Between F and V | Virtual | Upright | Magnified | Behind mirror |

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🧩 How to Draw Ray Diagrams (Optional):

To confirm these results, use three key rays:
1. Parallel ray → reflects through F.
2. Through F → reflects parallel.
3. Through C → reflects back on itself.

For example:
- In (4): All rays converge at C → real inverted image at C.
- In (5): Parallel rays emerge from F → diverge → virtual image at infinity.
- In (6): Rays diverge after reflection → virtual image behind mirror.

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Let me know if you'd like me to draw the ray diagrams or explain any part further!