Question

A convex lens has focal length of 30 cm. at what distance should object be placed from the

lens so that it forms an image at 60 cm on other side of the lens? Find the magnification

produced by the lens. ( v=- 60cm, m = -1)​

Answer 1

GiveN :

• Focal length (f) = 30 cm
• Image distance (v) = 60 cm

To FinD :

• Object position (u)
• Magnification of lens

SolutioN :

Use Lens formula :

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$\implies \boxed{\red{\rm{\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}}}}$

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$\implies \rm{\dfrac{1}{u} = \dfrac{1}{v} - \dfrac{1}{f}}$

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$\implies \rm{\dfrac{1}{u} = \dfrac{1}{60} - \dfrac{1}{30}}$

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$\implies \rm{\dfrac{1}{u} = \dfrac{1 - 2}{60}}$

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$\implies \rm{\dfrac{1}{u} = \dfrac{-1}{60}}$

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$\implies \rm{u \: = \: -60 \: cm}$

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$\underline {\sf{\therefore \: Object \: is \: placed \: at \: distance \: of \: 60 \: cm \: from \: lens}}$

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Now, use formula for magnification of lens :

$\implies \boxed{\blue{\rm{m = \dfrac{v}{u}}}}$

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$\implies \rm{m = \dfrac{60}{-60}}$

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$\implies \rm{m \: = \: -1}$

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$\underline{\sf{\therefore{Magnification \: of \: lens \: is \: -1}}}$

Answer 2

Given:-

• Focal Length (f) = 30cm

• Image Distance (v) = 60Cm

To Find:-

• Object Distance (u)

• Magnification

Solution:-

According to the Given Question

We have to calculate the object Distance. So

By using Lens Formula

⟹ 1/v -1/u = 1/f

Putting all the values which is given above

⟹ 1/60 -1/u = 1/30

⟹1/60 -1/30 = 1/u

⟹ 1 -2/60 = 1/u

⟹ -1/60 = 1/u

⟹ u = -60 cm

And Now ,

By using Magnification Formula

⟹ m = v/u

⟹m = -60/60

⟹ m = -1 cm

Thus, Magnification produced by lens is -1 cm