Question

a convex lens with focal length 30cm at what distance the object should be placed from lens so that it forms a image at 60cm in the other sider of lens find the magnification produce by the lens
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Answer 1

Answer:

The object should be placed at 60 cm on left side of the lens.

The magnification produced by the lens is - 1.

Explanation:

We have given that,

Focal length of convex lens ( f ) = 30 cm

Image distance ( v ) = 60 cm

We have to find,

Object distance ( u ) and

Magnification of lens ( M )

Now, we know that,

$\displaystyle{\pink{\sf\:\dfrac{1}{f}\:=\:\dfrac{1}{v}\:-\:\dfrac{1}{u}}\sf\:\:\:-\:-\:[\:Lens\:Formula\:]}$

$\displaystyle{\implies\sf\:\dfrac{1}{30}\:=\:\dfrac{1}{60}\:-\:\dfrac{1}{u}}$

$\displaystyle{\implies\sf\:\dfrac{1}{u}\:=\:\dfrac{1}{60}\:-\:\dfrac{1}{30}}$

$\displaystyle{\implies\sf\:\dfrac{1}{u}\:=\:\dfrac{30\:-\:60}{60\:\times\:30}}$

$\displaystyle{\implies\sf\:\dfrac{1}{u}\:=\:-\:\dfrac{3\cancel{0}}{180\cancel{0}}}$

$\displaystyle{\implies\sf\:\dfrac{1}{u}\:=\:-\:\cancel{\dfrac{3}{180}}}$

$\displaystyle{\implies\sf\:\dfrac{1}{u}\:=\:-\:\dfrac{1}{60}}$

$\displaystyle{\implies\sf\:-\:u\:=\:60}$

$\displaystyle{\implies\boxed{\red{\sf\:u\:=\:-\:60\:cm}}}$

The object should be placed at 60 cm on left side of the lens.

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Now,

$\displaystyle{\pink{\sf\:Magnification\:=\:\dfrac{Image\:height}{Object\:height}}}$

$\displaystyle{\implies\sf\:Magnification\:=\:\dfrac{v}{u}}$

$\displaystyle{\implies\sf\:Magnification\:=\:-\:\cancel{\dfrac{60}{60}}}$

$\displaystyle{\implies\boxed{\red{\sf\:Magnification\:=\:-\:1}}}$

The magnification produced by the lens is - 1.

From the negative sign of magnification, we can say that the nature of the image formed is real and inverted.