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 the object distance in the above case? (ii) Will the image be smaller or larger than the object? Draw a 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?

(i) To obtain an erect image using a concave mirror, the object should be placed within a certain range of distances from the mirror. The range of object distances for a concave mirror to produce an erect image depends on the focal length of the mirror.
For a concave mirror:
1) If the object is placed between the mirror’s surface and its focal point (F), the image will be virtual, erect, and larger than the object. This occurs for object distances less than the focal length (f).
2) If the object is placed at the focal point (F), the reflected rays are parallel, and there is no distinct image formed.
3) If the object is placed beyond the focal point (F), the image will be real, inverted, and smaller than the object.

Given that you want to obtain an erect image, the object should be within the range of distances where the image is virtual and erect. Therefore, the object distance (denoted as u) should be between the mirror’s surface and its focal point.

In this case, the focal length (f) of the concave mirror is given as 12 cm. So, the range of object distances (u) for obtaining an erect image is 0 <u <12 cm.

(ii) The image will larger than the object.
(iii) Image will be at 24cm in front of the mirror or the image is formed at C.
Diagram for (ii):