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Question
An object of height 10 cm is placed 25 cm away from the optical centre of a converging lens of focal length 15 cm. Calculate the image distance and height of the image formed.
Solution
Object height, O = +10 cm
Focal length, f = +15 cm
Object distance, u = −25 cm
Image distance, v = ?
Image height, I = ?
Using lens formula,
`1/"f" = 1/"v" -1/"u"`
`1/15 = 1/"v" -1/((-25))`
Or, `1/"v" = 1/15-1/25`
`1/"v" = (5 - 3)/75`
= `1/"v"=2/75`
v = `75/2`
Also, `(-"v")/"u"="I"/"O"`
Hence, `(75/2)/-25 = "I"/10`
`75/2 xx 1/-25 = "I"/10`
`3/-2 = "I"/10`
`-1.5 = "I"/10`
I = (-1.5) × 10 = −15 cm
Height of image is −15 cm, inverted.
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