A biro is placed at a distance of 10cm from a convex mirror of focal length 5cm.what is the position and nature of the image formed
To determine the position and nature of the image formed by the convex mirror, we can use the mirror formula:
1/f = 1/v - 1/u
Where:
f = focal length of the convex mirror = 5cm
v = image distance
u = object distance = -10cm (negative since it is placed on the same side as the object)
Substituting the given values into the formula, we have:
1/5 = 1/v - 1/-10
Multiply through by 5v to simplify:
v + 5v/10 = 1
10v + 5v = 10
15v = 10
v = 10/15
v = 2/3 cm
The positive value indicates that the image is formed on the opposite side of the mirror as the object. Therefore, the image is formed at a distance of 2/3 cm from the convex mirror.
To determine the nature of the image, we can consider the magnification of the mirror. The magnification (m) is given by:
m = -v/u
Substituting the known values:
m = -(2/3) / -10
m = 1/15
Since the magnification is positive and less than 1, the image formed by the convex mirror is diminished and upright. So, the nature of the image is virtual and diminished.