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. 

 

Answer:-

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