An object is placed at the following distances from a concave mirror of focal length 10 cm:
(a) 8 cm (b) 15 cm (c) 25 cm
Which position of the object will produce
a virtual image larger than the object ?

Answer

To determine the position of the object that will produce a virtual image larger than the object when using a concave mirror with a focal length of 10 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the properties of concave mirrors**:
- A concave mirror can produce both real and virtual images depending on the position of the object relative to the focal point (F) and the mirror's surface (the pole, P).
- The focal length (F) of the mirror is given as 10 cm.

2. **Identify the regions of image formation**:
- If the object is placed beyond the center of curvature (C, which is 20 cm from the mirror), the image is real and inverted.
- If the object is placed at the center of curvature (C), the image is real, inverted, and of the same size.
- If the object is placed between the center of curvature (C) and the focal point (F), the image is real, inverted, and reduced in size.
- If the object is placed at the focal point (F), the image is formed at infinity.
- If the object is placed between the focal point (F) and the pole (P), the image is virtual, erect, and enlarged.

3. **Determine the distances for the given object positions**:
- The distances provided are 8 cm, 15 cm, and 25 cm.
- The focal length is 10 cm, so we need to find which of these distances is between the focal point (10 cm) and the pole (0 cm).

4. **Analyze the distances**:
- For the distance of 8 cm: This is less than the focal length (10 cm), meaning the object is between the focal point and the pole. Therefore, it will produce a virtual image that is larger than the object.
- For the distance of 15 cm: This is beyond the focal length, meaning the image will be real and inverted.
- For the distance of 25 cm: This is also beyond the focal length, meaning the image will be real and inverted.

5. **Conclusion**:
- The only distance that produces a virtual image larger than the object is when the object is placed at 8 cm from the concave mirror.

### Final Answer:
The object should be placed at **8 cm** from the concave mirror to produce a virtual image that is larger than the object.