Explain how mirrors can produce images that are larger or smaller than life size, as well as upright or inverted

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Explain how mirrors can produce images that are larger or smaller than life size, as well as upright or inverted

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Orla Orla 4 years 2021-09-03T05:03:15+00:00 1 Answers 6 views 0

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  1. ngocdiep
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    2021-09-03T05:04:20+00:00
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    Answer:

    1) When d_{o} < d_{i} (hence  d_{o} < f ) and they are both in front of the mirror (positive), the image will be larger and inverted

    2) When d_{o} > d_{i} (and d_{o} < f ) such that they are both positive (in front of the mirror), the image will be smaller and inverted

    3) When the image is behind the mirror, for convex mirrors and the object is in front the image will be uptight. The magnification of the image will be the ratio of the image distance to the object distance from the mirror

    Explanation:

    The position of an object in front of a concave mirror of radius of curvature, R, determines the size and orientation of the image of the object as illustrated in the mirror equation

    \dfrac{1}{f}=\dfrac{1}{d_{o}} + \dfrac{1}{d_{i}}

    Magnification, \, m = \dfrac{h_{i}}{h_{o}} = -\dfrac{d_{i}}{d_{o}}

    Where:

    f = Focal length of the mirror = R/2

    d_{i} = Image distance from the mirror

    d_{o} = Object distance from the mirror

    h_{i} = Image height

    h_{o} = Object height

    d_{o} is positive for an object placed in front of the mirror and negative for an object placed behind the mirror

    d_{i} is positive for an image formed in front of the mirror and negative for an image formed behind the mirror

    m is positive when the orientation of the image and the object is the same

    m is negative when the orientation of the image and the object is inverted

    f and R are positive in the situation where the center of curvature is located in front of the mirror (concave mirrors) and f and R are negative in the situation where the center of curvature is located behind the mirror (convex mirrors)

    ∴ When d_{o} < d_{i} (hence  d_{o} < f ) and they are both in front of the mirror (positive), the image will be larger and inverted

    When d_{o} > d_{i} (and d_{o} < f ) such that they are both positive (in front of the mirror), the image will be smaller and inverted

    When the image is behind the mirror, for convex mirrors and the object is in front the image will be uptight. The magnification of the image will be the ratio of the image distance to the object distance from the mirror.

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