## An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained? Find the size and the nature of the image.

### Q. 15 :- An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained? Find the size and the nature of the image.

Focal length, f = – 18 cm
Object-distance, u = – 27 cm
Height of object, h1′= 5 cm
Image-distance, v = ?
Height of image h2′= ?

 1 1 1 + = v u f 1 1 1 + = v − 27 -18 15 − 1 1 1 = + v 18 27 1 − 3 + 2 1 = = v 54 54 60 v = = 54 cm 7

The screen should be kept at a distance of 54 cm in front of mirror

 h2 − v m = = h1 u h2 (− 54 ) => = = 7 cm (− 27 ) (− 54 ) × 7 cm => h2 = (− 27 ) Height (Size ) of Image = h2 = 2 × 7 cm = 14 cm cm

Thus, a 14 cm high, virtual and an inverted image is formed