A bright object and a viewing screen are separated by a dist

A bright object and a viewing screen are separated by a distance of 78 cm. At what locations between the object and the screen should a lens of focal length 14 cm be placed in order to produce a crisp image on the screen? [Hint: First draw a diagram.]

nearest distance from the object cm

farthest distance from the object cm

Solution

1/f = 1/u +1/v.
Or
f = uv/(u+v)
Given f = 14 and [u+v] =78
uv = f*( u+v) = 14*78 = 1092
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To find u , substitute for v = [64- u]
u[78- u] = 1092.
u^2 -78u +1092 = 0
u = (39-429) or u = (39+429)
u = 18.28 or 59.71 cm
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nearest distance from the object 18.28cm
farthest distance from the object 59.71cm
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