Dividing a plot into multiple plots by y-axis intervals and finding the midpoint value of each graph

Question

I'm new to Mathematica. I have a Plot that I would like to divide evenly at the y-axis. I can divide evenly at x-axis if I set the min and max range of x.

But, how do I do that at the y-axis, and how do I show the midpoint (x,y values) of each graph?

I would like to show part of the graph when for eg: Plot situation at y-axis from 0-0.2 / 0.2-0.4 / 0.4-0.6 and so forth...but without changing the plotrange that have been set

Here is the code

k = 155900;
F3 = Plot[
  Sqrt[2] √(√(1/m1^2 + 
         20 Sqrt[3118] (1/m1)^(3/2) Sqrt[1/50] + 
         3118020 Sqrt[3118] Sqrt[1/m1] (1/50)^(3/2) + 
         24304810001/50^2 + 623602/(m1 50)) - 
      10 Sqrt[3118] Sqrt[1/m1] Sqrt[1/50] - k/50)
  , {m1, 5, 500}
  , PlotRange -> {{0, 500}, {0, 1}}
  , AxesLabel -> {m1, SuperStar[E]}
  ]

Answer 1

Perhaps this will work for you.

With[{k = 155900},
  Column[
    Table[
      Plot[
        Sqrt[2] 
          Sqrt[
            Sqrt[1/m1^2 + 20 Sqrt[3118] (1/m1)^(3/2) Sqrt[1/50] + 
              3118020 Sqrt[3118] Sqrt[1/m1] (1/50)^(3/2) + 
              24304810001/50^2 + 623602/(m1 50)] - 
            10 Sqrt[3118] Sqrt[1/m1] Sqrt[1/50] - k/50], 
        {m1, 5, 500},
        PlotRange -> {All, interval},
        AxesLabel -> {m1, SuperStar[E]}],
      {interval, Partition[Range[0., .6, .2], 2, 1]}]]]

Answer 2

k = 155900;
GraphicsColumn@Table[
  Show[Plot[
    Sqrt[2] \[Sqrt](\[Sqrt](1/m1^2 + 
           20 Sqrt[3118] (1/m1)^(3/2) Sqrt[1/50] + 
           3118020 Sqrt[3118] Sqrt[1/m1] (1/50)^(3/2) + 
           24304810001/50^2 + 623602/(m1 50)) - 
        10 Sqrt[3118] Sqrt[1/m1] Sqrt[1/50] - k/50), {m1, 5, 500}, 
    PlotRange -> {{0, 500}, r}, AxesLabel -> {"m1", SuperStar[E]}],
   PlotRange -> {{0, 500}, {0, 1}}, 
   AxesOrigin -> {0, 0}], {r, {{.4, .8}, {.2, .4}, {0, .2}}}]

Answer 3

expr = Sqrt[2] √(√(1/m1^2 + 20 Sqrt[3118] (1/m1)^(3/2) Sqrt[1/50] + 
     3118020 Sqrt[3118] Sqrt[1/m1] (1/50)^(3/2) + 24304810001/50^2 + 623602/(m1 50)) - 
     10 Sqrt[3118] Sqrt[1/m1] Sqrt[1/50] - k/50);

Using ConditionalExpression:

Row[Plot[ConditionalExpression[expr, # <= expr <= #2], {m1, 5, 500}, 
    PlotRange -> {{0, 500}, {0, 1}}, AxesLabel -> {m1, SuperStar[E]}, 
    ImageSize -> 300] & @@@ {{0.4, 0.8}, {0.2, 0.4}, {0., 0.2}}]

Using MeshFunctions and MeshShading:

Row[Plot[expr, {m1, 5, 500}, MeshFunctions -> {#2 &}, 
    MeshShading -> {None, Blue}, Mesh -> {#},   MeshStyle -> Opacity[0],
    PlotRange -> {{0, 500}, {0, 1}}, AxesLabel -> {m1, SuperStar[E]}, 
    ImageSize -> 300] & /@ {{0.4, 0.8}, {0.2, 0.4}, {0., 0.2}}]