Question

What is a mirror's radius of curvature if cars 19.0 m away appear 0.25 their normal size? follow the sign conventions?

Answer 1

We have two equation for the mirror:
$\frac{1}{f}=\frac{1}{d_0}-\frac{1}{d_i}\\ M=-\frac{d_i}{d_0}$
Index i denotes an image, and index 0 denotes the object. 
In our case, magnification is 0.25:
$0.25=-\frac{d_i}{d_0}\\ -0.25d_0=d_i; d_0=19m\\ d_i=-0.25\cdot 19=-4.75m$
We plug this back into the first equation:
$\frac{1}{f}=\frac{1}{19}-\frac{1}{4.75}\\ f=-3.80m\\ R=2f=-7.6m$