An observer stands at the edge of a rectangular Olympic pool of uniform actual depth. a$)$ What is the reflection coefficient of the freshwater$/$air boundary at normal incidence? How does it compare to the reflection coefficient of the glass$/$air boundary at normal incidence? $(5$ pt$)$ b$)$ Does the pool appear deeper or shallower than it is$?$ Why? Does the effect get stronger or weaker with horizontal distance between the observer and a point of interest at the bottom of the pool? $(5$ pt$)$ c$)$ What is the perceived depth h of the pool as seen by the observer, at his feet, i$.$e$.$ at close to normal incidence, compared to the actual depth H$,$ i$.$e$.$ what is h$/$H$?(10$ pt$)$ d$)$ The pool$$s length is $50$ meters and its actual depth is H$=2$ m$.$ The observer$$s viewing point is at H$=2$ m above the freshwater surface. Calculate the perceived depth h as a function of horizonal distance R between the observer$$s viewpoint and the point of interest at the bottom of the pool, for R$=0,10,20,30,40,50$ m$.$