Clear[f,  xpt,  m,  apparent]
f[x_]  :=  ((Sqrt[2500  +  (x^2)])/30.0) + ((Sqrt[2500  +  (((200  -  x))^2)])/22.5)
xpt  =  Solve[(∂_x) f[x]  ==  0,  x]

Question 1:  The light ray should cross the water's surface at the point x = 149.411.

m  =  -50/x  /.  xpt;
apparent  =  50  +  m * 200

Question 2:  The apparent position of the object is at the point (200, -16.9293).

Clear[f,  xpt,  m,  apparent,  a]
a  =  -40;
f[x_]  :=  ((Sqrt[2500  +  (x^2)])/30.0) + ((Sqrt[(a^2)  +  (((200  -  x))^2)])/22.5)
xpt  =  
        Solve[(∂_x) f[x]  ==  0,  
          x];
m  =  -50/x  /.  xpt;
apparent  =  50  +  m * 200

Clear[f,  xpt,  m,  apparent,  a]
a  =  -30;
f[x_]  :=  ((Sqrt[2500  +  (x^2)])/30.0) + ((Sqrt[(a^2)  +  (((200  -  x))^2)])/22.5)
xpt  =  
        Solve[(∂_x) f[x]  ==  0,  
          x];
m  =  -50/x  /.  xpt;
apparent  =  50  +  m * 200

Clear[f,  xpt,  m,  apparent,  a]
a  =  -20;
f[x_]  :=  ((Sqrt[2500  +  (x^2)])/30.0) + ((Sqrt[(a^2)  +  (((200  -  x))^2)])/22.5)
xpt  =  
        Solve[(∂_x) f[x]  ==  0,  
          x];
m  =  -50/x  /.  xpt;
apparent  =  50  +  m * 200

Clear[f,  xpt,  m,  apparent,  a]
a  =  -10;
f[x_]  :=  ((Sqrt[2500  +  (x^2)])/30.0) + ((Sqrt[(a^2)  +  (((200  -  x))^2)])/22.5)
xpt  =  
        Solve[(∂_x) f[x]  ==  0,  
          x];
m  =  -50/x  /.  xpt;
apparent  =  50  +  m * 200

Question 3:  The apparent positions of the four new points are:

(200, -12.8787),  (200, -9.18927),  (200, -5.83262), and
(200, -2.77927).
    
They are not equally spaced.