An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature and size.

Q. 14 :- An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature and size. 

 

Answer:-

Radius of curvature, R = + 30 cm
Focal length, f = R/2 = + 30/2 cm = + 15 cm
Object-distance, u = – 20 cm
Height of object
h1′= 5 cm
Image-distance, v = ? Height of image h2′= ?

1 1 1

+
=
v u f
1 1 1

+
=
v − 20 + 15
1 1 1

=
+
v 15 20
1 4 + 3 7

=
=
v 60 60
60
v =
= 8.57 cm
7

The image is formed behind the mirror at a distance of 8.6 cm 

h2 − v
m =
=
h1 u
h2 8.57
=> =
=
5 cm 20
8.57 × 5 cm
= h2 =
20
Height (Size )

of Image

= h2 = 2.175 cm

Thus, a 2.175 cm high, virtual and erect image is formed