Page 149 - NCERT Science Class 10 English Medium

Example 9.1
A convex mirror used for rear-view on an automobile has a radius of
curvature of 3.00 m. If a bus is located at 5.00 m from this mirror,
find the position, nature and size of the image.

Solution
Radius of curvature, R = + 3.00 m;
Object-distance, u = – 5.00 m;
Image-distance, v = ?
Height of the image, h′= ?

3.00 m
Focal length, f = R/2 = + = + 1.50 m (as the principal focus of
2
a convex mirror is behind the mirror)
1 1 1
Since + =
v u f

1 1 1 1 1 1 1
or, = − = + – = +
v f u 1.50 ( 5.00) 1.50 5.00
−
5.00 1.50
+
=
7.50
+ 7.50
v = = + 1.15 m
6.50
The image is 1.15 m at the back of the mirror.

h ' v 1.15 m
Magnification, m = = − = –
h u − 5.00 m
= + 0.23
The image is virtual, erect and smaller in size by a factor of 0.23.

Example 9.2
An object, 4.0 cm in size, is placed at 25.0 cm in front of a concave
mirror of focal length 15.0 cm. At what distance from the mirror
should a screen be placed in order to obtain a sharp image? Find
the nature and the size of the image.
Solution
Object-size, h = + 4.0 cm;
Object-distance, u = – 25.0 cm;
Focal length, f = –15.0 cm;
Image-distance, v = ?
Image-size, h′ = ?
From Eq. (10.1):

1 1 1
+ =
v u f
1 1 1 1 1 1 1
or, = − = − = − +
v f u − 15.0 − 25.0 15.0 25.0

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