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Question
An object 50 cm tall is placed on the principal axis of a convex lens. Its 20 cm tall image is formed on the screen placed at a distance of 10 cm from the lens. Calculate the focal length of the lens.
Solution
Height of object (h) = 50 cm
Height of image (h') = -20 cm (real and inverted)
Distance of image from the lens (v) = 10 cm
Distance of object from the lens (u) = ?
Focal length of the lens (f)= ?
We know, magnification (m) of the lens is given by:
m=`v/u=(h')/h`
Thus, substituting the values of v, h and h', we get:
`10/u=(-20)/50 `
`10/u=(-20)/50`
`u=(-5)/2x10`
∴ u=-25 cm
Using the lens formula:
`1/v-1/u=1/f`
`1/10-1/-25=1/f`
⇒`1/10+1/25=1/f`
⇒`(5+2)/5=1/f`
⇒`7/50=1/f`
⇒`f=50/7`
⇒`f=7.14`cm.
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