Answer to Question #155909 in Optics for best

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:


"\\dfrac{1}{d_o}+\\dfrac{1}{d_i}=-\\dfrac{1}{f},""\\dfrac{1}{d_o}+\\dfrac{1}{d_i}=-\\dfrac{2}{R},""d_i=\\dfrac{1}{-\\dfrac{2}{R}-\\dfrac{1}{d_o}},""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:


"\\dfrac{h_i}{h_o}=-\\dfrac{d_i}{d_o},""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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