Consider the situation described in problem $1$ where light emerges horizontally from ground level. Take $k=0\mathrm{.}0020m^{-1}$ and $n_0=1\mathrm{.}0001$ and find at which horizontal distance, $x,$ the ray reaches a height of $y=1\mathrm{.}5m.($Answer $55$ m $)$

As a woman, who's eyes are $h=1\mathrm{.}5m$ above the ground, looks down the road sees a tree with height $H=9\mathrm{.}0m.$ Below the tree is what appears to be a reflection of the tree. The observation of this apparent reflection gives the illusion of water on the roadway. This effect is commonly called a mirage. Use the results of questions $1$ and $2$ and the principle of ray reversibility to analyze the diagram below. Assume that light leaving the top of the tree bends toward the horizontal until it just grazes ground level. After that, the ray bends upward eventually reaching the woman's eyes. The woman interprets this incoming light as if it came from an image of the tree. Determine the size, $H^{\text{'}},$ of the image. $($Answer $8\mathrm{.}8$ m $)$