## Objects are closer than they appear?

The statement "objects are closer than they appear" in a car's convex mirror is not technically correct. Prove this using the equation.
Isn't it correct? A convex mirror gives you a wider field of view to overcome the passenger side blind spot. The wider the view, the smaller the object, giving the false impression that the objects in question are more distant than they are.

Even math agrees with me.
$\frac{1}{-f}=\frac{1}{do}+\frac{1}{di}$
do is distance from the object to the mirror, and di is the distance from the image to the mirror.
$\frac{hi}{ho}=\frac{di}{do}=m$
hi is height of the image and ho is height of the object. m is magnification.

Let's say that ho=1.5, f=-2.5 (for a convex mirror the focal point is negative), and do=2.5
$\frac{1}{-2.5}=\frac{1}{2.5}+\frac{1}{di}$
$\frac{1}{-2.5}-\frac{1}{2.5}=\frac{1}{di}$
$\frac{1}{-2.5}-\frac{1}{2.5}=0.8=$
$\frac{1}{0.8}=-1.25=di$
So di is equal to -1.25

Moving on....
$\frac{hi}{1.5}=\frac{1.25}{2.5}$
$\frac{1.25}{2.5}=0.5$
$1.5*0.5=0.75=hi$
So the image is half its size! If we were to view this image in the mirror, it would appear to be farther away because we intrinsically know that an object will appear smaller the farther away it is.