An object is placed 64.0 cm from a screen. (a) Where should a converging lens of

Question

An object is placed 64.0 cm from a screen.
(a) Where should a converging lens of focal length 6.0 cm be placed to form an image on the screen?
shorter distance____cm from the screen
farther distance____cm from the screen
(b) Find the magnification of the lens.
magnification if placed at the shorter distance____
magnification if placed at the farther distance____
(Please show the algebra to calculate the answers)

Explanation / Answer

Let lens is placed at a distance x cm from the screen =>v=x [ image distance] u=64-x [ object distance] 1/u + 1/v=1/f =>1/(64-x)+1/x= 1/6 =>64*6 = 64x-x^2 x^2-64x+384=0 solving for x = 6.7 cm or x=57.29 cm b) magnification if x= 6.7 = -v/u= -6.7/(64-6.7)=-0.1169 for long distance= -57.9/(64-57.9)=-9.49

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