Question

the focal length of a convex lens is 40cm. if an object is kept at a distance of 60cm from the lens,then find the image distance and magnification produced by the lens
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Answer 1

Given :

▪ Focal length = 40cm

▪ Distance of object = 60cm

▪ Type of lens : convex

To Find :

▪ Distance of image (v)

▪ Magnification (m)

Formula :

✴ Lens formula :

$\bigstar\:\underline{\boxed{\bf{\pink{\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}}}}}$

✴ Formula of lateral magnification :

$\bigstar\:\underline{\boxed{\bf{\green{m=\dfrac{v}{u}}}}}$

Calculation :

⚾ Distance of image (v) :

$\implies\sf\:\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}\\ \\ \implies\sf\:\dfrac{1}{v}-\dfrac{1}{(-60)}=\dfrac{1}{40}\\ \\ \implies\sf\:\dfrac{1}{v}=\dfrac{1}{40}-\dfrac{1}{60}\\ \\ \implies\sf\:\dfrac{1}{v}=\dfrac{20}{2400}\\ \\ \implies\boxed{\bf{\gray{v=120\:cm}}}$

⚾ Magnification :

$\mapsto\sf\:m=\dfrac{v}{u}\\ \\ \mapsto\sf\:m=\dfrac{120}{(-60)}\\ \\ \mapsto\boxed{\bf{\orange{m=-2}}}$

⏭ Nature of image :

• Real
• Inverted

⏭ Size of image :

• Enlarged