QuestionMay 1, 2025

When you hold a spherical concave mirror with a 48.2-cm radius of curvature 39.5 cm in front of your face, you see an image of your face that is 61.8 cm in front of the mirror. What is the magnification of this image? -0.639 -1.56 1.56 0.639

When you hold a spherical concave mirror with a 48.2-cm radius of curvature 39.5 cm in front of your face, you see an image of your face that is 61.8 cm in front of the mirror. What is the magnification of this image? -0.639 -1.56 1.56 0.639
When you hold a spherical concave mirror with a 48.2-cm radius of curvature 39.5 cm in front of your face, you see an image of your face that is 61.8
cm in front of the mirror. What is the magnification of this image?
-0.639
-1.56
1.56
0.639

Solution
4.1(200 votes)

Answer

1. Calculate the focal length ### The focal length is half the radius of curvature. Use f = \frac{R}{2}: f = \frac{48.2}{2} = 24.1 cm. ## Step2: Apply the mirror equation ### Use \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} to find magnification: \frac{1}{24.1} = \frac{1}{39.5} + \frac{1}{61.8}. Solve for \frac{1}{d_o}: \frac{1}{d_o} = \frac{1}{24.1} - \frac{1}{61.8} = 0.04149. d_o = \frac{1}{0.04149} = 39.5
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