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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​

Answer»

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.


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