QuestionJuly 19, 2025

Find the location of an image when the object is located 15.0 cm from a concave mirror. The mirror has a focal length of 20.0 cm. A. 5.00 cm B. -15.0cm C. 60.0 cm D. -60.0 cm

Find the location of an image when the object is located 15.0 cm from a concave mirror. The mirror has a focal length of 20.0 cm. A. 5.00 cm B. -15.0cm C. 60.0 cm D. -60.0 cm
Find the location of an image when the object is located 15.0 cm from a concave mirror. The mirror has a focal length of 20.0 cm. A. 5.00 cm B. -15.0cm C. 60.0 cm D. -60.0 cm

Solution
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Answer

-8.57 cm Explanation 1. Use the mirror formula The mirror formula is **\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}**, where f is the focal length, d_o is the object distance, and d_i is the image distance. 2. Substitute known values Given f = -20.0 cm (concave mirror, so focal length is negative) and d_o = 15.0 cm. Substitute these into the formula: \frac{1}{-20} = \frac{1}{15} + \frac{1}{d_i}. 3. Solve for d_i Rearrange to find \frac{1}{d_i} = \frac{1}{-20} - \frac{1}{15}. Calculate: \frac{1}{d_i} = -\frac{3}{60} - \frac{4}{60} = -\frac{7}{60}. Thus, d_i = -\frac{60}{7} \approx -8.57 cm.

Explanation

1. Use the mirror formula<br /> The mirror formula is **$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$**, where $f$ is the focal length, $d_o$ is the object distance, and $d_i$ is the image distance.<br />2. Substitute known values<br /> Given $f = -20.0$ cm (concave mirror, so focal length is negative) and $d_o = 15.0$ cm. Substitute these into the formula: $\frac{1}{-20} = \frac{1}{15} + \frac{1}{d_i}$.<br />3. Solve for $d_i$<br /> Rearrange to find $\frac{1}{d_i} = \frac{1}{-20} - \frac{1}{15}$. Calculate: $\frac{1}{d_i} = -\frac{3}{60} - \frac{4}{60} = -\frac{7}{60}$. Thus, $d_i = -\frac{60}{7} \approx -8.57$ cm.
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