An object is originally placed a certain distance from a convexlens having a foc

Question

An object is originally placed a certain distance from a convexlens having a focal length of 50 cm, producing a real image. Now the object is moved so that it is half as far away fromthe lens as it was originally, producing in this case a virtualimage. In both cases, the absolute values of the imagedistances are the same. Calculate the original distance fromthe object to the lens. please show all work!
An object is originally placed a certain distance from a convexlens having a focal length of 50 cm, producing a real image. Now the object is moved so that it is half as far away fromthe lens as it was originally, producing in this case a virtualimage. In both cases, the absolute values of the imagedistances are the same. Calculate the original distance fromthe object to the lens. please show all work! please show all work!

Explanation / Answer

Here focal length(f)=+50cm Also let absolute value of image distance be v Then when it is real , image distance will be positive . Let initial object distance be -u . Then using the lens formula for initial case , (1/V) - (1/U) = (1/f) Putting , (1/v) + (1/u) = (1/50) ........(i) When image is virtual , image distance will be negative . object distance be -u/2 . Then using the lens formula for final case , (1/V) - (1/U) = (1/f) Putting , -(1/v) + (2/u) = (1/50) ........(ii) Adding (i) and (ii) 3/u = 2/50 u = 75 cm So original distance of the object is 75 cm

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