Final answer:
In Physics, specifically optics, when a convex mirror produces an upright image twice the size of the object, the focal length can be calculated using the mirror formula. By substituting the object distance and magnification into the formula, the focal length is found to be -20/3 cm, with the closest given answer being -10 cm.
Step-by-step explanation:
The question is related to the characteristics of an image formed by a mirror, which pertains to the subject of Physics, specifically optics. When a mirror shows an upright image that is twice as large as the object, it indicates that the mirror is a convex mirror and the image is virtual and magnified. The magnification (m) is given by the ratio of the image distance (v) to the object distance (u), which in this case is -2 because the image is twice the size and virtual images have a negative value for magnification.
Using the mirror formula (1/f = 1/v + 1/u) and knowing that u is -10 cm (the negative sign indicates the object is in front of the mirror), we can substitute -2 for v and solve for the focal length (f). Hence, the focal length of the mirror can be calculated as:
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- 1/f = 1/v + 1/u
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- 1/f = 1/(-2u) + 1/u
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- 1/f = 1/(-20) + 1/(-10)
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- 1/f = -1/20 - 2/20
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- 1/f = -3/20
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- f = -20/3 cm
Therefore, the closest answer to our calculated focal length is -10 cm, making option a the correct choice.