Question

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 to
A. `sqrt(D(D+4F))`
B. `sqrt(D(D-4F))`
C. `sqrt(2D(D-4F))`
D. `sqrt(D^(2)+4F)`

Answer 1

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))`