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An object of length 0.5 cm is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position, nature and size of the image.
Here, h = 5 cm = height of an object
R = Radius of curvature = 30 cm
∴
f = R/2
f = 30/2
f = 15 cm
v = -20 cm
v = ?, h' = ?
Using mirror formula,
1/f = 1/u + 1/v
∴ 1/v = 1/f - 1/u
1/v = 1/15 + 1/20
1/v = 7/60
⇒ v = 60/7
v = 8.57 cm
The distance of image is 8.57 cm behind the mirror.
Magnification m = h'/h = -(v/u)
∴ h' = -(v/u) x h
h' = - 60/7 x 1/(-20) x 5
h' = 15/7
h' = 2.17
h' = 2.2 cm
Image formed is small, virtual and erect in nature.
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