Question #155909

an object 7m high is placed 15cm from a convex spherical mirror of radius of curvature 45cm.describe its image


1
Expert's answer
2021-01-15T13:46:52-0500

Let's first find the image distance of the convex mirror from the mirror equation:


1do+1di=1f,\dfrac{1}{d_o}+\dfrac{1}{d_i}=-\dfrac{1}{f},1do+1di=2R,\dfrac{1}{d_o}+\dfrac{1}{d_i}=-\dfrac{2}{R},di=12R1do,d_i=\dfrac{1}{-\dfrac{2}{R}-\dfrac{1}{d_o}},di=1245 cm115 cm=9 cm=0.09 m.d_i=\dfrac{1}{-\dfrac{2}{45\ cm}-\dfrac{1}{15\ cm}}=-9\ cm=-0.09\ m.

The sign minus means that the image is virtual and formed behind the mirror.

Let's find the image height from the magnification equation:


hiho=dido,\dfrac{h_i}{h_o}=-\dfrac{d_i}{d_o},hi=hodido=7 m(0.09 m)0.15 m=4.2 m.h_i=h_o\dfrac{-d_i}{d_o}=7\ m\cdot\dfrac{-(-0.09\ m)}{0.15\ m}=4.2\ m.

The sign plus means that the image is upright and diminished.

Answer:

The image is 4.2 m high, virtual, upright, diminished and formed behind the mirror.


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