We wish to obtain an erect image of an object, using a concave mirror of focal length 15 cm. What should be the range of distance of the object from the mirror? What is the nature of the image? Is the image larger or smaller than the object? Draw a ray diagram to show the image formation in this case.
The object should be placed between the pole (P) and the focus (F) of the concave mirror. Since the focal length is 15 cm, the range of distance of the object from the mirror should be between 0 cm and 15 cm.
The nature of the image is virtual and erect.
The image is larger (enlarged) than the object.
A ray diagram would show: (1) A concave mirror with principal axis marked, (2) Focus (F) at 15 cm and Centre of curvature (C) at 30 cm from the pole, (3) An object placed between P and F, (4) A ray from the top of the object parallel to the principal axis, which after reflection passes through F, (5) A ray from the top of the object directed towards C, which reflects back along the same path, (6) The reflected rays appear to diverge from a point behind the mirror, forming a virtual, erect, and enlarged image.
Explanation
According to Table 9.1 in the context, when an object is placed between P and F (between the pole and focus) of a concave mirror, the image formed is behind the mirror, enlarged, and virtual and erect in nature. This is the only position where a concave mirror produces an erect image. Since the focal length is given as 15 cm, the object must be placed at a distance less than 15 cm from the mirror to obtain an erect image.