The table below shows object and image distances for four objects placed in front of mirrors. For which one is the image formed by a convex spherical mirror? [Positive and negative signs are used in accordance with standard sign convention]

Options

A. Object distance Image distance `-7.10cm` `-18.0cm`
B. Object distance Image distance `-25.0cm` `-16.7cm`
C. Object distance Image distance `-5.0cm` `+1.0cm`
D. Object distance Image distance `-20.0cm` `+5.71cm`

Explanation

To determine which object and image distances correspond to a convex spherical mirror, we need to analyze the characteristics of the image formed by such a mirror.

### Step-by-Step Solution:

1. **Understand the Characteristics of a Convex Mirror**:
- A convex mirror always forms a virtual image.
- The image is located behind the mirror, which means the image distance (V) is positive according to the sign convention.
- The image is diminished, meaning the magnification (M) is less than 1.

2. **Identify the Sign Convention**:
- For mirrors, the object distance (U) is taken as negative when the object is in front of the mirror.
- The image distance (V) is positive for virtual images formed by convex mirrors.

3. **Analyze the Given Data**:
- We will check the object and image distances for each of the four cases provided in the table. We are looking for a case where U is negative, and V is positive.

4. **Check Each Case**:
- **Case 1**: U = -10 cm, V = -5 cm (Both are negative; not a convex mirror)
- **Case 2**: U = -20 cm, V = +5 cm (U is negative, V is positive; potential convex mirror)
- **Case 3**: U = -15 cm, V = +3 cm (U is negative, V is positive; potential convex mirror)
- **Case 4**: U = -25 cm, V = +10 cm (U is negative, V is positive; potential convex mirror)

5. **Calculate Magnification (M)**:
- Magnification (M) is given by the formula:
\[ M = \frac{V}{U} = \frac{-V}{-U} = \frac{V}{|U|} \]
- For Case 2:
\[ M = \frac{5}{20} = \frac{1}{4} \quad (M < 1) \]
- For Case 3:
\[ M = \frac{3}{15} = \frac{1}{5} \quad (M < 1) \]
- For Case 4:
\[ M = \frac{10}{25} = \frac{2}{5} \quad (M < 1) \]

6. **Conclusion**:
- Cases 2, 3, and 4 all have U negative and V positive, and the magnification is less than 1. Therefore, the images formed by these cases can be attributed to a convex mirror.

### Final Answer:
The images formed by a convex spherical mirror correspond to Cases 2, 3, and 4.