# A convex lens has a focal length of 10 cm. At what distance from the lens should the object be placed so that it forms a real and inverted

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A convex lens has a focal length of 10 cm. At what distance from the lens should the object be placed so that it forms a real and inverted image 20 cm away from the lens? What would be the size of the image formed if the object is 2 cm high? With the help of a ray diagram show the formation of the image by the lens in this case.

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According to the question;

Object distance = u;

Image distance (v) = 20cm;

Focal length = 10cm

By lens formula;

$\frac1v-\frac1u=\frac1f$

⇒ $\frac1{20}-\frac1u=\frac1{10}$

⇒ $\frac1{u}=\frac1{20}-\frac1{10}$

⇒ $\frac1{u}=\frac{1-2}{20}-\frac{-1}{20}$

⇒ $\frac1{u}=\frac{-1}{10}$

⇒ u = -20cm.

Therefore, object is placed at 20 cm in front of lens.

Now;

Height of object h1= 2cm;

Magnification = $\frac{h_2}{h_1}=\frac{v}u$

Putting values of v and u

Magnification = $\frac{h_2}{2}=\frac{20}{-20}$

⇒ $\frac{h_2}{h_1}= -1;$

⇒ h2 = 2 x -1 = -2

Height of image is 2 cm.

Negative sign means image is inverted.

Thus, the image is real, inverted and same as size of object.

Diagram below shows the image formation.