7. A convex spherical mirror, whose focal length has a magni- tude of 15.0 cm, is to form an image 10.0 cm behind the mir- ror. (a) Where should the object be placed? (b) What is the magnification of the mirror?

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In the following problem, algebraic signs are not given. We leave it to you to determine the correct sign to use with each quantity, based on an analysis of the problem and the sign conventions in Table 23.1.

**Question 7: Convex Spherical Mirror Problem**

A convex spherical mirror, whose focal length has a magnitude of 15.0 cm, is to form an image 10.0 cm behind the mirror. 

(a) Where should the object be placed? 

(b) What is the magnification of the mirror?

---

This problem involves understanding how convex mirrors form images and how to apply the mirror formula and magnification formula to determine object distance and magnification. Make sure to use these principles carefully for accurate calculations.
Transcribed Image Text:**Question 7: Convex Spherical Mirror Problem** A convex spherical mirror, whose focal length has a magnitude of 15.0 cm, is to form an image 10.0 cm behind the mirror. (a) Where should the object be placed? (b) What is the magnification of the mirror? --- This problem involves understanding how convex mirrors form images and how to apply the mirror formula and magnification formula to determine object distance and magnification. Make sure to use these principles carefully for accurate calculations.
### Table 23.1 Sign Conventions for Mirrors

| Quantity         | Symbol | In Front | In Back | Upright Image | Inverted Image |
|------------------|--------|----------|---------|---------------|----------------|
| Object location  | \( p \)   | \( + \)      | \( - \)       |               |                |
| Image location   | \( q \)   | \( + \)      | \( - \)       |               |                |
| Focal length     | \( f \)   | \( + \)      | \( - \)       |               |                |
| Image height     | \( h' \)  |            |               | \( + \)         | \( - \)          |
| Magnification    | \( M \)   |            |               | \( + \)         | \( - \)          |

**Explanation:**

This table outlines the sign conventions used when analyzing mirrors, which is essential for calculations in optics.

- **Object Location (\( p \)):**
  - Positive (\( + \)): When the object is in front of the mirror.
  - Negative (\( - \)): When the object is behind the mirror.

- **Image Location (\( q \)):**
  - Positive (\( + \)): When the image is in front of the mirror.
  - Negative (\( - \)): When the image is behind the mirror.

- **Focal Length (\( f \)):**
  - Positive (\( + \)): For concave mirrors.
  - Negative (\( - \)): For convex mirrors.

- **Image Height (\( h' \)):**
  - Positive (\( + \)): When the image is upright.
  - Negative (\( - \)): When the image is inverted.

- **Magnification (\( M \)):**
  - Positive (\( + \)): When the image is upright.
  - Negative (\( - \)): When the image is inverted.

These conventions help in determining the nature and position of images formed by mirrors.
Transcribed Image Text:### Table 23.1 Sign Conventions for Mirrors | Quantity | Symbol | In Front | In Back | Upright Image | Inverted Image | |------------------|--------|----------|---------|---------------|----------------| | Object location | \( p \) | \( + \) | \( - \) | | | | Image location | \( q \) | \( + \) | \( - \) | | | | Focal length | \( f \) | \( + \) | \( - \) | | | | Image height | \( h' \) | | | \( + \) | \( - \) | | Magnification | \( M \) | | | \( + \) | \( - \) | **Explanation:** This table outlines the sign conventions used when analyzing mirrors, which is essential for calculations in optics. - **Object Location (\( p \)):** - Positive (\( + \)): When the object is in front of the mirror. - Negative (\( - \)): When the object is behind the mirror. - **Image Location (\( q \)):** - Positive (\( + \)): When the image is in front of the mirror. - Negative (\( - \)): When the image is behind the mirror. - **Focal Length (\( f \)):** - Positive (\( + \)): For concave mirrors. - Negative (\( - \)): For convex mirrors. - **Image Height (\( h' \)):** - Positive (\( + \)): When the image is upright. - Negative (\( - \)): When the image is inverted. - **Magnification (\( M \)):** - Positive (\( + \)): When the image is upright. - Negative (\( - \)): When the image is inverted. These conventions help in determining the nature and position of images formed by mirrors.
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