Question

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.​

Answer 1

The focal length of the convex lens is,

$\sf{f=+10cm}$

The image distance is, $\sf{v=+20cm}$

The height of the object, $\sf{O=2cm}$

As the image distance is positive, thus, the image formed will be real and inverted.

Consider the formula that relates the focal length of the lens, image distance and object distance.

$\sf{ \dfrac{1}{f} = \dfrac{1}{v} -\dfrac{1}{u} }$

• Where f is the focal length, v is the image distance and u is the object distance.
• Where f is the focal length, v is the image distance and u is the object distance.Substitute the values in the above equation.

$\sf{ \dfrac{1}{10} = \dfrac{1}{20} -\dfrac{1}{u} }$

$\dashrightarrow \sf{ \dfrac{1}{u} = \dfrac{1}{20} -\dfrac{1}{10} }$

$\sf{ \dashrightarrow∴ \dfrac{1}{u} = \dfrac{1}{20} }$

Therefore, the object distance is 20 cm.

The value of the object distance is twice that of the focal length of the convex lens. So, the object is placed at 2F and the image also forms at 2F on the other side of the lens, as the image distance equals the object distance. Thus, the height of the image will be 2 cm.

The formation of the image by drawing a ray diagram is given in attachment.

∴ The distance from the lens at which the object is placed so that forms a real and inverted image 20 cm away from the lens is 20 cm. The size of the image formed if the object is 2 cm high is the same as that of the size of the object.

Hope it will help u.

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