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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.

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Solution

According to the question:
Image distance, v=20 cm
Focal length, f=10 cm (positive since convex lens)
Let the object distance be u

By lens formula:
1v1u=1f
120 cm1u=110 cm
1u=120 cm110 cm
1u=1220 cm=120 cm
1u=120 cm
u=20 cm

Therefore, the object is placed at 20 cm away from the lens, opposite to the image side.

Now,
Height of object, h1=2 cm
Magnification, m=h2h1=vu

Putting values of v and u:
Magnification, m=h22 cm=20 cm20 cm
h22 cm=1
h2=2 cm
Height of image is 2 cm, and the negative sign means the image is inverted.

Thus, the image is real, inverted and same as the size of the object.
The ray diagram shows the image formation.

1631480_1417373_ans_9036a60d7ab94ff2b188da85bb897dca.png

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