Rays from sun converge at a point 15 cm in front of a concave mirror. Where should an object be placed so that size of its image is equal to the size of the object ?

Options

A. 15 cm in front of the mirror
B. 30 cm in front of the mirror
C. Between 15 cm and 30 cm in front of the mirror
D. More than 30 cm in front of the mirror.

Answer

To solve the problem of where to place an object in front of a concave mirror so that the size of its image is equal to the size of the object, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The rays from the sun converge at a point 15 cm in front of the concave mirror. This point is the focal point (F) of the mirror.
- Therefore, the focal length (f) of the concave mirror is -15 cm (the negative sign indicates that it is a concave mirror).

2. **Determine the Relationship Between Focal Length and Radius of Curvature**:
- The radius of curvature (R) of a concave mirror is related to its focal length by the formula:
\[ R = 2f \]
- Substituting the focal length:
\[ R = 2 \times (-15) = -30 \text{ cm} \]
- The radius of curvature is -30 cm, indicating that the center of curvature (C) is 30 cm in front of the mirror.

3. **Identify the Position for the Object**:
- To have the size of the image equal to the size of the object, the object must be placed at the center of curvature (C).
- When an object is placed at the center of curvature, the image formed is real, inverted, and of the same size as the object.

4. **Conclusion**:
- Therefore, the object should be placed at a distance of 30 cm in front of the mirror (at the center of curvature) to ensure that the size of the image is equal to the size of the object.

### Final Answer:
The object should be placed **30 cm in front of the concave mirror**.

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