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An object of size 7.0 cm is placed at a distance of 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed so that a clear focused image of the object is formed? Find the size and nature of an object.
Height of an object h1 = 5 cm
Object distance u = – 27 cm
Focal length = – 18 cm
Height of an image h1 = ?
Image distance u = ?
From the formula :
⇒ 1/u + 1/v = 1/f
⇒ 1/(-27) + 1/v = 1/(-18)
⇒ 1/v = 1/18 + 1/27
⇒ - (3+2)/ 54
⇒ -1/54
⇒ v = –54 cm
Therefore, screen should be placed at a distance of 54 cm from the screen.
m = h2/h1 = - v/u
⇒ h2/7 = -54/-27
⇒ h2/7 = 2
⇒ h2 = 14 cm
Thus, the height of the image formed is 14 cm and is real and inverted in nature.
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