\"An object is placed 54 cm from a screen. At what points between object and scr

Question

"An object is placed 54 cm from a screen. At what points between object and screen may a lens 12 cm focal length be placed to obtain an image on the screen? Show the complete derivation of all equations used to solve this problem as well as complete calculations" "An object is placed 54 cm from a screen. At what points between object and screen may a lens 12 cm focal length be placed to obtain an image on the screen? Show the complete derivation of all equations used to solve this problem as well as complete calculations"

Explanation / Answer

Lens Formula =
  
1/object distance (do) + 1/image distance (di) = 1/focal length.
1/u + 1/v = 1/f.

Let us assume We keep lens at distance x from object, Therefore do = x;
Then Distance of image from lens = 54 - x ;

Focal length of mirror = 12cm.

Substituting values into lens equation.

1/x + 1/(54-x) = 1/12
x^2 - 54x + 648 = 0

Solving for x

X comes out to be = 18 cm & 36 cm

Lens can be kept at distance 18 cm & 36 cm from object.

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