A luminous object and a screen are at a fixed distance D apart. A converging lens of focal length f is placed between the object and screen. A real image of the object in formed on the screen for two lens positins if they are separated by a distance d equal toA. `sqrt(D(D+4F))`B. `sqrt(D(D-4F))`C. `sqrt(2D(D-4F))`D. `sqrt(D^(2)+4F)`

A luminous object and a screen are at a fixed distance D apart. A conv

1.	A luminous object and a screen are at a fixed distance D apart. A converging lens of focal length f is placed between the object and screen. A real image of the object in formed on the screen for two lens positins if they are separated by a distance d equal toA. `sqrt(D(D+4F))`B. `sqrt(D(D-4F))`C. `sqrt(2D(D-4F))`D. `sqrt(D^(2)+4F)`
Answer» Correct Answer - b. Let the objec distance be x. The, the image distance is `D-x`. From lens equation, `(1)/(x)+(1)/(D-x)=(1)/(f)` On algebraic rearrangement, we get `x^(2)-Dx+Df=0` On solving for x, we get `x_(1)=(D-sqrt(D(D-4f)))/(2)` `x_(2)=(D+sqrt(D(D-4f)))/(2)` The distance between the two object position is `d=x_(2)-x_(1)=sqrt(D(D-4f))`

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