The figure below gives the lateral magnification m of an object versus the objec

Question

The figure below gives the lateral magnification m of an object versus the object distance p from a spherical mirror as the object is moved along the mirror's central axis through a range of values for p. (The horizontal axis is marked in increments of 10 cm.) What is the magnification of the object when the object is 190 cm from the mirror?
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The figure below gives the lateral magnification m of an object versus the object distance p from a spherical mirror as the object is moved along the mirror's central axis through a range of values for p. (The horizontal axis is marked in increments of 10 cm.) What is the magnification of the object when the object is 190 cm from the mirror?

Explanation / Answer

1/f = 1/p + 1/q

==> 1/q = 1/f - 1/p

==> q = (f p)/(p - f)

M = -q/p = -((f p)/(p - f))/p = f/(f - p)

at p = 0.50 m:

==> M = 0.5

==> 0.5 = f/(f - 0.50)

==> f = -0.5 m

at p = 190 cm

M = f/(f - p) = 0.5/(0.5 - 1.90) = -0.357

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