An object is located in a fixed position in front of a screen. Sharp image is obtained on the screen for two positions of a thin lens separated by 10 cm . The size of the images in two situations are in the ratio 3: 3 . What is the distance between the screen and the object?

Step-by-step solution

Given: Separation of lens for two of its position, d=10 ~cm Ratio of size of the images in two positions I₁ I₂ = 3 2 Distance of object from the screen, D= ? Applying formula, aligned & I₁ I₂ = (D+d)^2 (D-d)^2 & 3 2 = (D+10)^2 (D-10)^2 & 3 2 = D^2+100+20 D D^2+100-20 D & 3 D^2+300-60 D=2 D^2+200+40 D & D^2-100 D+100=0 aligned On solving, we get D=99 ~cm Hence the distance between the screen and the object is 99 ~cm .