A 3.92 cm tall object is placed in 31.3 cm in front of a convex mirror. The focal length is 12.7 cm. What is the magnification of the

Question

A 3.92 cm tall object is placed in 31.3 cm in front of a convex mirror. The focal
length is 12.7 cm. What is the magnification of the image?

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Thu Nguyệt 5 years 2021-08-30T01:14:36+00:00 1 Answers 11 views 0

Answers ( )

  1. ngocdiep
    0
    2021-08-30T01:15:37+00:00
    Reply

    Answer:

    0.29

    Explanation:

    We can find the position of the image by using the mirror equation:

    \frac{1}{f}=\frac{1}{p}+\frac{1}{q}

    where:

    f is the focal length of the mirror

    p is the distance of the object from the mirror

    q is the distance of the image from the mirror

    For the mirror in this problem:

    f = -12.7 cm (the focal length of a convex mirror is negative)

    p = 31.3 cm (distance of the object)

    Solving for q, we find the position of the image:

    \frac{1}{q}=\frac{1}{f}-\frac{1}{p}=\frac{1}{-12.7}-\frac{1}{31.3}=-0.111 cm^{-1}\\q=\frac{1}{-0.111}=-9.1 cm

    And so, the magnification of the image is:

    M=-\frac{q}{p}

    And substituting,

    M=-\frac{-9.1}{31.3}=0.29

    Which means that the image is upright (positive sign) and diminished (M is smaller than 1).

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