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there was a question in which the object is place right side of a concave lens so I decided as usual like taking objects position as positive and considering the right face of the concave mirror so I take focal length also as positive but my answer was wrong I want the reason?

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Imagine a bunch of rays travelling parallel to the principle axis and diverge after travelling through the lens. If you had to take the focal length to be positive you would have to trace it on the positive side which is not possible. When you trace the paths of the diverging rays to find which is the spot of convergence you end up at the focal point which is on the negative side by convention. A simple ray diagram should help you understand this

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  • $\begingroup$ Yeah, but I said that the object is on right side so according to you the ray will diverge on right side and focal length will be positive......actually this is a question in which a virtual object formed on right side of the concave lens but my answer is wrong why? $\endgroup$ Commented Oct 21, 2019 at 2:12
  • $\begingroup$ The rays will diverge on the right side but that doesn't determine the sign to be assigned to the focal length. It is where those rays will be converging. So if the rays are diverging on the right side it is imperative that they will never converge on the right side because they are always moving apart. What remains is that they shall converge on the left side. A visual aid should help. Cheers! kbcc.cuny.edu/academicdepartments/physci/science25/documents/…. $\endgroup$ Commented Oct 21, 2019 at 5:54

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