Question

an object placed at a distance of do from a convex lens which produces a real image of magnification 3 . At what distance must the object be placed to produce a virtual image of magnification 3 ?

Answer 1

@hartnn help me please

Answer 2

Think about the lens equation, and magnification equation:
\[1/d_{o}+1/d_{i}=1/f\]\[M=-d_{o}/d_{i}\]When you are solving this problem, remember you can cancel the focal length because it is the same for the first and second tests. That will leave you with a relationship between the distance of the object and image for each test. However, you know the magnification and can use that to get the distance of the image in terms of the distance of the object. Plugging this in, you now have a relationship between the distance of the object for the real image and distance of the object for the virtual image. Now all you need to do is simplify.

Here is a algebra hint:
\[1/d_{o}+1/d_{i}=1/f \rightarrow f=d_{o}d_{i}/(d_{o}+d_{i})\]