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A light bulb sits 0.75 m from a convex lens with a 0.50 m focal length. Using d_i equals f d_o over (d_o minus f), what image distance and magnification result?
Ad_i = 1.5 m, m = -2.0, a real, inverted, enlarged image
Bd_i = 1.5 m, m = 2.0, a virtual, upright, enlarged image
Cd_i = 0.30 m, m = -0.4, a real, inverted, reduced image
Dd_i = -1.5 m, m = 2.0, a virtual, upright, enlarged image
Answer & Solution
Correct answer: A. d_i = 1.5 m, m = -2.0, a real, inverted, enlarged image
1. Using d_i = (f d_o) / (d_o - f) = ((0.50)(0.75)) / (0.75 - 0.50) = 0.375 / 0.25 = 1.5 m.
2. The positive image distance means the image is real, formed on the far side of the lens from the object.
3. Magnification is m = -d_i / d_o = -1.5 / 0.75 = -2.0.
4. A negative magnification means the image is inverted, and a magnitude greater than one means it is enlarged.
5. d_i = -1.5 m would wrongly make the image virtual, which cannot happen when the object sits beyond the focal length of a converging lens.
6. d_i = 0.30 m does not follow from substituting these object distance and focal length values into the equation.
_Source: OpenStax Physics (CC BY 4.0), Ch 16 "Mirrors and Lenses", section 16.3 Lenses_
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