# A CONVEX LENS PRODUCES AN IMAGE ON SCREEN TWICE THE SIZE OF THE OBJECT. THE DISTANCE B/W OBJECT & SCREEN IS 45 CM. CALCULATE THE OBJECT DISTANCE. PLZ EXPLN IN DETAIL IN STEPS,...... The path of the light rays is in the figure below. The convention signs for distances object-lens, image-lens and height of the object and image are also depicted in the attached figure.

The equation of the lens is

`1/x_1 +1/x_2 =1/f` , with `f >0` for convergent lenses.

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The path of the light rays is in the figure below. The convention signs for distances object-lens, image-lens and height of the object and image are also depicted in the attached figure.

The equation of the lens is

`1/x_1 +1/x_2 =1/f` , with `f >0` for convergent lenses.

From similar triangles `ABO` and `A'B'O` one can write for the magnification:

`|M| =|-y_2/y_1| = x_2/x_1`

Thus `2x_1 =x_2`

and from the original condition given in the problem text that

`x_1+x_2 =45`

one obtains

`x_2/2 +x_2 =45`

`3/2*x_2 =45`

`x_2 =(2*45)/3 =90/3 =30 cm`

`x_1 =45-30 =15 cm`

Answer: the object distance is `x_1 =15 cm`

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