A converging lens ( f = 23.9 cm) is used to project animage of an object onto a

Question

A converging lens (f = 23.9 cm) is used to project animage of an object onto a screen. The object and the screen are97.5 cm apart, and between them the lens can be placed at either oftwo locations. Find the two object distances, the smaller being theanswer to part (a).

Explanation / Answer

Given      distance S = x from the object.     S1 = 97.5cm - x     f = 23.9cm           f =SS1/S+S1    -->23.9cm = (x)(97.5cm-x)/(x+97.5cm-x)       -->23.9 cm =(x*97.5cm-x^2) /97.5cm       --> 2330.25 cm2 =(97.5cm) x -x2            x2 - (97.5cm)x + 2330.25cm2 =0           Solving for x , we getx =41.94cm or x =55.56cm     Thus, these are the object distances

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