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.

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#### 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.

Concept: Convex Lens

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