An object is placed at the following distances from a concave mirror of focal length 10 cm : (a) 8 cm (b) 15 cm © 20 cm (d) 25 cm.

Which position of the object will produce :

(i) a diminished real image ?

(ii) a magnified real image ?

(iii) a magnified virtual image.

(iv) an image of the same size as the object ?

Given focal length of mirror = 10 cm

Therefore, distance of centre of curvature = 20 cm

(i) A diminished real image is formed by a concave mirror when the object lies beyond C. Here, C is at 20 cm. Therefore, the diminished real image will be formed when the object is at a distance greater than 20 cm, which in this problem is 25 cm. Hence, the position of the object for a diminished real image is 25 cm.

(ii) A magnified real image is formed by a concave mirror when the object is between F and C. Here, F is at 10 cm and C is at 20 cm. Hence, the magnified real image will be formed when the object lies between 10 cm and 20 cm which in this problem is 15 cm. Therefore, the position of object for a magnified real image is 15 cm.

(iii) A magnified virtual image is formed by a concave mirror when the object is within focus (F) at a distance less than focal length or less than 10 cm, which in this problem is 8 cm. Therefore, the position of object for a magnified virtual image is 8 cm.

(iv) An image of the same size as object is formed by a concave mirror when the object lies at the centre of curvature ©. Here, C is at 20 cm, therefore, the image of the same size ‘ as the object will be formed when the object is at 20 cm from the concave mirror. Thus, the position of the object for an image of same size as the object is 20 cm.