More mirrors. Object O stands on the central axis of a spherical or plane mirror

Question

More mirrors. Object O stands on the central axis of a spherical or plane mirror. For this situation (see the table below, all distances are in centimeters), find (a) the type of mirror, (b) the focal length of the mirror (including sign), (c) the radius of curvature r (nonzero number or 0 if infinity), (d) the image distance i, whether (e)the image is real or virtual, (f) inverted or noninverted from O, and (g) on the same side of the mirror as object O or on the opposite side.

Explanation / Answer

here the magnification m = -p/i

i = -m*p = -(-0.9*14)

i = 12.6 cm

from mirror equation

1/i + 1/p = 1/f

1/12.6 + 1/14 = 1/f

f = 6.63 cm

r = 2f = 13.26 cm

real

inverted

opposite

(a)       (b)           (c)    (d)         (e)    (f)    (g)  

Type        f           r          p          i     m    R/V    I/NI    Side

concave   6.63 cm     13.26cm     +14         12.6 cm   -0.90    R       I      opposite

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