QuestionJuly 16, 2025

A 3.0 cm object is 12.0 cm from a convex mirror that has a focal length of 20.0 cm. What is the distance of the image from the mirror? -7.5cm What is the height of the image? square cm

A 3.0 cm object is 12.0 cm from a convex mirror that has a focal length of 20.0 cm. What is the distance of the image from the mirror? -7.5cm What is the height of the image? square cm
A 3.0 cm object is 12.0 cm from a convex mirror that has a focal length of 20.0 cm. What is the distance of the image from the mirror? -7.5cm What is the height of the image? square cm

Solution
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Answer

1.875 cm Explanation 1. Use Mirror Formula The mirror formula is **\frac{1}{f} = \frac{1}{v} + \frac{1}{u}**. Here, f = -20.0 cm (convex mirror), u = -12.0 cm (object distance). Solve for v (image distance). 2. Substitute and Solve for Image Distance \frac{1}{-20} = \frac{1}{v} + \frac{1}{-12}. Solving gives v = -7.5 cm. 3. Use Magnification Formula Magnification m = \frac{h_i}{h_o} = -\frac{v}{u}. Given h_o = 3.0 cm, v = -7.5 cm, u = -12.0 cm. 4. Calculate Height of the Image m = -\frac{-7.5}{-12} = \frac{7.5}{12}. Thus, h_i = m \times h_o = \frac{7.5}{12} \times 3.0 cm.

Explanation

1. Use Mirror Formula<br /> The mirror formula is **$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$**. Here, $f = -20.0$ cm (convex mirror), $u = -12.0$ cm (object distance). Solve for $v$ (image distance).<br /><br />2. Substitute and Solve for Image Distance<br /> $\frac{1}{-20} = \frac{1}{v} + \frac{1}{-12}$. Solving gives $v = -7.5$ cm.<br /><br />3. Use Magnification Formula<br /> Magnification $m = \frac{h_i}{h_o} = -\frac{v}{u}$. Given $h_o = 3.0$ cm, $v = -7.5$ cm, $u = -12.0$ cm.<br /><br />4. Calculate Height of the Image<br /> $m = -\frac{-7.5}{-12} = \frac{7.5}{12}$. Thus, $h_i = m \times h_o = \frac{7.5}{12} \times 3.0$ cm.
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