Type of mirror and nature of image

The child is using a concave mirror. The nature of the image observed is virtual, erect, and magnified.

Range of distance of the mirror from his face

The range of distance of the mirror from his face can be calculated using the mirror formula:

1/f = 1/u + 1/v

Where f is the focal length, u is the distance of the object from the mirror, and v is the distance of the image from the mirror.

Since the image is virtual and erect, v will be negative. The magnification, m, can be calculated using the formula:

m = -v/u

where m is the magnification.

Using these formulas, we can calculate the range of distance of the mirror from the child's face to be between 7.5 cm and 30 cm.

Ray diagram

To draw a ray diagram, we can take the following steps:

1. Draw the principal axis of the mirror.

2. Mark the focal point on the principal axis.

3. Draw a ray from the top of the child's face parallel to the principal axis. This ray will reflect off the mirror and pass through the focal point.

4. Draw a ray from the top of the child's face through the focal point. This ray will reflect off the mirror parallel to the principal axis.

5. The intersection of these two rays represents the virtual, erect, and magnified image of the child's face.

Explanation

A concave mirror is a type of mirror that curves inward, like a bowl. When an object is placed in front of a concave mirror, the mirror reflects the light rays back towards a point called the focal point. If the object is placed beyond the focal point, the mirror will reflect the light rays back towards a virtual image that is magnified and erect.

In this case, the child is using a concave mirror with a focal length of 15 cm. The distance of the mirror from the child's face can be calculated using the mirror formula, which takes into account the focal length of the mirror, the distance of the object from the mirror, and the distance of the image from the mirror. The range of distance of the mirror from the child's face is between 7.5 cm and 30 cm.

To draw a ray diagram, we can use the rules of reflection to trace the path of two rays of light from the top of the child's face to the mirror and back to the child's eye. The intersection of these two rays represents the virtual, erect, and magnified image of the child's face.

In conclusion, the child is using a concave mirror to observe a virtual, erect, and magnified image of his face. The range of distance of the mirror from his face is between 7.5 cm and 30 cm, and a ray diagram can be used to illustrate the path of light rays from the object to the mirror and back to the observer.

The mirror used by child is a concave mirror.
The nature of image is virtual and magnified.
The range of face from mirror is between focal length and pole.