Question

An object is located 12.5 cm in front of a convex mirror, the image being 6.90...

An object is located 12.5 cm in front of a convex mirror, the image being 6.90 cm behind the mirror. A second object, twice as tall as the first one, is placed in front of the mirror, but at a different location. The image of this second object has the same height as the other image. How far in front of the mirror is the second object located?

Homework Answers

Answer #1

We have 1/f = 1/do + 1/di from this we get the focal length of the mirror

so f = do*di/(do + di) = 12.5*(-6.9)/(12.5 + -6.9) = -15.4cm

Now m= -di/do for the first object m = 6.9/12.5 = 0.55

Since m = also = yi/yo we have yi/yo = 0.55 so yi = 0.55*yo

Since the second object is twice the first but the image height is the same we get
m = -di/do = 0.275 or di = -0.275*do

We now have 1/(-15.4) = 1/(do) + 1/di = 1/do + 1/(-0.275*do)

-0.0649 = (-0.275 + 1)/(-0.275*do) = 0.71/(-0.29*do)

so do = 37.765cm

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