A candle is located 30 cm in front of a concave spherical mirror having principal focus f = 10 cm, as shown in the diagram below. What is the image distance? [ Select ] 15 cm 7.5 cm 0.067 cm -30 cm What is the magnification? [ Select ] -2.0 x -0.5 x -7.5 x -1.0 x What are the image characteristics? [ Select ] real, reduced, and inverted virtual, reduced, and upright real, enlarged, and inverted virtual, enlarged, and inverted

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First, we restate the problem and the choices to be analyzed: A candle is located 30 cm in front of a concave spherical mirror with focal length f = 10 cm. We are asked for (1) the image distance, (2) the magnification, and (3) the image characteristics. The answer options provided for each are: - Image distance options: 15 cm, 7.5 cm, 0.067 cm, -30 cm - Magnification options: -2.0 x, -0.5 x, -7.5 x, -1.0 x - Image characteristics options: real, reduced, and inverted; virtual, reduced, and upright; real, enlarged, and inverted; virtual, enlarged, and inverted Option 1 (image distance): '15 cm' — Why this could be correct or not depends on the sign convention used. Using the common convention where object distance u is taken as positive for a real object in front of the mirror and focal length f is positive for a concave mirror, the mirror equation is 1/f = 1/v + 1/u. Substituting f = 10 cm and u = 30 cm gives 1/v = 1/f − 1/u = 0.1 − 0.0333… = 0.0667, so v = 15 cm. This yields......Login to view full explanation

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