Question

A bright object and a viewing screen are separated by a distance of 89.0 cm . Part A At what distance(s) from the object should a lens of focal length 17.0 cm be placed between the object and the screen in order to produce a crisp image on the screen? Express your answer using three significant figures. If there is more than one answer, enter your answers in ascending order separated by commas.

Answer 1

1/f = 1/u +1/v.
Or
f = uv/(u+v)
Given f = 17 and [u+v] =89
uv = f*( u+v) = 17*89 = 1513
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To find u , substitute for v = [89- u]
u[89- u] = 1513.
u^2 -89u +1513 = 0  
u = 22.9 or 66.12 cm
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nearest distance from the object 22.9 cm
farthest distance from the object 66.12cm