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Question
An object 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.
Solution
Object distance, u = – 20 cm
Object height, h = 5 cm
Radius of curvature, R = 30 cm
Radius of curvature = 2 × Focal length
R = 2f
f = `30/2`
f = 15 cm
According to the mirror formula,
`1/"f" = 1/"v" + 1/"u"`
`1/15 = 1/"v" + 1/(-20)`
`1/15 = 1/"v" - 1/20`
`1/15 + 1/20 = 1/"v"`
`1/"v" = (4 + 3)/60`
`1/"v" = 7/60`
v = `60/7`
v = 8.57 cm
The positive value of v indicates that the image is formed behind the mirror.
The positive value of magnification indicates that the image formed is virtual.
Size of the image:
m = `"h'"/"h" = -"v"/"u"`
`"h'"/5 = (-8.57)/(-20)`
20 h' = 8.57 × 5
20 h' = 42.9
h' = `42.85/20`
h' = 2.14 cm
The positive value of image height indicates that the image formed is erect.
Therefore, the image formed is virtual, erect, and smaller in size.
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