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Following is a problem from book: "The near point of a person's eye is 53.0 cm. To see objects clearly at a distance of 24.0 cm, what should be the focal length of the appropriate corrective lens?"

My book says the image distance(from the center of lens) is negative. Why is that so? Isn't the image distance negative when an image is formed on the same side of the object? However, isn't that not the case. My understanding of the scenario is that the lens is in between the object and the image. With object on one side of lens and image on opposite.

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  • $\begingroup$ Didn't they meant that the object distance is negative, it is said "To see objects clearly at a distance of -24.0 cm" $\endgroup$ – Vaishakh Sreekanth Menon Mar 4 at 3:48
  • $\begingroup$ No, I accidentally inserted a negative sign there. I edited my question. $\endgroup$ – Hema_D Mar 4 at 4:19
  • $\begingroup$ In many conventions in optics, distances to virtual images are given as negative numbers. $\endgroup$ – Pieter Mar 4 at 23:53
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The corrective lens produces an image at the near point (or further) so that the person can see it.

In your question the object is at 24 cm but near point is 53 cm , So the person can see the image only if the object is at 53 cm or beyond, what the corrective lens does is that it produces an image(Say I1) of the object(which is at 24 cm) at 53 cm (or beyond) ,This image I1 acts as the object for the eye, since the image formed by the corrective lens is on same side of object it is negative by sign convention.

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