THE ACTUAL PROBLEM: A vessel of depth H is filled with a non-homogenous liquid whose refractive index varies with y as u=(2 -(y/H)), where y is measured from bottom of the vessel. Find the apparent depth as seen by an observer from above? (Paraxial approximation is allowed) RELEVANT EQUATIONS: We know in paraxial approximation u1/x=u2/y Where u1 is refractive index of medium 1, x is object distance from surface, u2 is refractive index of surrounding medium , y2 is apparent depth. MY ATTEMPT: I took a differential strip of thickness dy at a height of y from bottom. its refractive index is (2-(y/H)-(dy/H)) and refractive index of element just below it is (2-(y/H)) Now, Lets say that the image of the bottom of the vessel formed by refraction from all strips below this height y be at a distance x from the bottom. Therefore, Its distance from the strip is y-x. So using the formulae i mentioned. (2-y/H)/(y-x)= [(2-(y/H)-(dy/H))]/[y-x-dx)] So ydx/H -2dx=-ydy/H+xdy/H. After this am struck cause I cannot integrate. I know other ways of solving this problem(mentioned in my text book), but I wanna know what exactly am I doing wrong here? Any help/inputs will be really appreciated.