To obtain an erect image using a concave mirror with a given focal length, let's analyze the situation step-by-step:
1. Given Data:
- Focal length of the concave mirror (f) = 15 cm.
2. Conditions for Erect Image Formation:
- For a concave mirror to form an erect image, the object must be placed between the pole (P) and the principal focus (F) of the mirror.
- This setup ensures that the image formed is virtual, erect, and magnified.
3. Range of Object Distance:
- The pole (P) of the mirror is at distance 0 cm.
- The principal focus (F) is at distance 15 cm from the mirror.
- Therefore, the object should be placed between 0 cm (just before the pole) and 15 cm (at the focal point).
Hence, the range of distances for the object placement to get an erect image is from 0 cm to 15 cm.
4. Nature of the Image:
- The image formed will be virtual and erect since a concave mirror can form a virtual image only when the object is placed between the pole and the focus.
5. Size of the Image:
- The image formed will be larger than the object because, under these conditions, a concave mirror magnifies the image.
To summarize, the range of distances for the object from the mirror is 0 cm to 15 cm. The nature of the image is virtual and erect, and the image is larger than the object.
6. Ray Diagram:
We will draw a ray diagram to illustrate how the image is formed in this scenario.
- Draw a concave mirror with its principal axis.
- Mark the pole (P), the focus (F) at 15 cm from the pole, and the center of curvature (C), which is at 30 cm from the pole (2F).
- Place the object (denoted by an arrow) between the pole P and the focus F.
- Draw a ray parallel to the principal axis from the object to the mirror. This ray reflects back through the focus F.
- Draw another ray passing through the center of curvature C. Since it passes through the center, it will reflect back on itself.
- Extend the reflected rays backward to meet at a point behind the mirror. This is where the virtual image is formed.
Here's a simple representation of the ray diagram:
```
----|----|----|---- P ---- F ---- | ----|---- C
Object (concave mirror) Image (virtual, erect, and larger)
```
In the real ray diagram:
- The concave mirror lies with its reflective side facing towards the left.
- The object is an arrow pointing upwards between P and F.
- The reflected rays are extended behind the mirror to show the virtual image formed behind the mirror as an upward-pointing arrow larger than the object.
