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:

`(1)/(f)=(1)/(d_0)-(1)/(d_i)\\ M=-(d_i)/(d_0)`
Index i denotes an image, and index 0 denotes the object.
In our case, magnification is 0.25:

`0.25=-(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:

`(1)/(f)=(1)/(19)-(1)/(4.75)\\ f=-3.80m\\ R=2f=-7.6m`