It is desired to obtain an erect image of an object, using concave mirror of focal length of 12 cm. (i) What should be the range of distance of an object placed in front of the mirror? (ii) Will the image be smaller or larger than the object. Draw ray diagram to show the formation of image in this case. (iii) Where will the image of this object be, if it is placed 24 cm in front of the mirror? Draw ray diagram for this situation also to justify your answer. Show the positions of pole, principal focus and the centre of curvature in the above ray diagrams.

(i) Range of Object Distance

To obtain an erect image using a concave mirror, the object must be placed between the pole ($P$) and the principal focus ($F$) of the mirror.

Given that the focal length $f = 12\text{ cm}$, the range of distance of the object from the mirror should be between $0\text{ cm}$ and $12\text{ cm}$ (i.e., $0 < u < 12\text{ cm}$).

(ii) Size and Ray Diagram of the Image

The image formed in this case will be larger than the object (enlarged/magnified) and virtual.

(iii) Object Placed at $24\text{ cm}$

If the object is placed at $24\text{ cm}$ in front of the mirror:

• Since the focal length $f = 12\text{ cm}$, the radius of curvature is $R = 2f = 2 \times 12\text{ cm} = 24\text{ cm}$.
• This means the object is placed exactly at the centre of curvature ($C$).
• According to the laws of reflection and image formation rules, when an object is placed at $C$, its image is also formed at $C$ (i.e., at a distance of $24\text{ cm}$ in front of the mirror).
• The image will be real, inverted, and of the same size as the object.