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Question
An object of size 7.0 cm is placed at 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 sharp focused image can be obtained? Find the size and the nature of the image.
Solution
Object distance, u = −27 cm
Object height, h = 7 cm
Focal length, f = −18 cm
Using the mirror formula, we get
`1/"f" = 1/"v" + 1/"u"`
⇒ `1/"v" = 1/"f" - 1/"u"`
⇒ `1/"v" = 1/(-18) - 1/(-27)`
⇒ `1/"v" = -1/18 + 1/27`
⇒ `1/"v" = (-3 + 2)/54`
⇒ `1/"v" = (-1)/54`
⇒ v = −54 cm
Thus, the distance of the image 'v' is 54 cm.
Now, using the magnification formula, we get,
Size of the image:
m = `"h'"/"h" = -"v"/"u"`
`"h'"/5 = -((-54))/((-27))`
`"h'"/7` = −2
h' = −2 × 7
h' = −14 cm
Negative sign of h' shows that the image is inverted.
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