Let a positive convex decreasing differentiable function $f(x)$ be defined on $\mathbb{R}$ and $\lim_{x \to \infty}f(x)=0$. Let the point light source be placed at $P(x_0,y_0)$ with $y_0>0,\,y_0 <f(x_0)$. Light is assumed to be reflected from the plot $y=f(x)$ and the $x$-axis. Does there exist a number $R$ s. t. the part of the graph $y=f(x)$ for $x>R$ is not lightened?
A model example $f(x):=e^{-x},\,P(0,0.5)$ suggests the answer is yes.