I NEED HELP PLEASE, THANKS! :) A 20.0 cm tall object is placed 50.0 cm in front of a convex mirror with a radius of curvature of 34.0

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I NEED HELP PLEASE, THANKS! 🙂
A 20.0 cm tall object is placed 50.0 cm in front of a convex mirror with a radius of curvature of 34.0 cm. Where will the image be located, and how tall will it be? Please show all work.

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Diễm Kiều 3 years 2021-08-22T13:22:51+00:00 1 Answers 26 views 0

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  1. mocmien2
    0
    2021-08-22T13:24:50+00:00
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    Answer:

    i = -12.7 cm; h =  5.07 cm

    Explanation:

    1. Find the focal length

    The focal length of a concave spherical mirror is half of its radius of curvature.

    f = ½r = ½ × 34.0 cm = 17.0 cm

    2. Find the image distance

    A convex mirror produces a virtual image behind the mirror, so the image distance is negative.

    \begin{array}{rcl}\dfrac{1}{o} + \dfrac{1 }{i} & = & \dfrac{1}{f}\\\\\dfrac{1}{50.0} + \dfrac{1 }{i} & = & \dfrac{1}{-17.0}\\\\\dfrac{1}{i} & = & \dfrac{1}{-17.0} - \dfrac{1}{50.0}\\\\& = & \dfrac{50.0 - (-17.0)}{500\times(-17.0)}\\\\& = & \dfrac{67.0}{-850}\\\\i & = & \dfrac{-850}{67.0}\\\\& = & \textbf{-12.7 cm}\\\end{array}

    3. Find the image size

    \begin{array}{rcl}\\\\\dfrac{h_{\text{i}}}{ h_{\text{o}}} & = & -\dfrac{i}{o} \\\\\dfrac{h_{\text{i}}}{ 20.0} & = & -\dfrac{-12.7}{50.0} \\\\h_{\text{i}} & = & 20.0 \times \dfrac{12.7}{50.0}\\\\& = & \textbf{5.07 cm}\\\end{array}

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