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A person stands 6.0 m from a convex security mirror and sees a virtual image that appears to be 1.0 m behind the mirror. Taking the object distance as positive and the virtual image distance as negative, what is the mirror's focal length?
A-1.2 m
B1.2 m
C-7.0 m
D6.0 m
Answer & Solution
Correct answer: A. -1.2 m
1. The object distance is d_o = 6.0 m, taken as positive since the person stands in front of the mirror.
2. The image is virtual, so its distance is negative: d_i = -1.0 m.
3. Using f = (d_i d_o) / (d_o + d_i) gives f = ((-1.0)(6.0)) / (6.0 + (-1.0)).
4. The numerator is -6.0 and the denominator is 5.0, so f = -6.0 / 5.0 = -1.2 m.
5. The negative sign is exactly what is expected for a convex mirror, whose focal point lies behind the mirror.
6. 1.2 m without the negative sign would wrongly describe a concave mirror instead of this convex one.
7. 6.0 m repeats the object distance rather than solving the equation, and is not a focal length at all.
_Source: OpenStax Physics (CC BY 4.0), Ch 16 "Mirrors and Lenses", section 16.1 Reflection_
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