Create a detailed, well-labeled, and technically accurate diagram using Python and Matplotlib to visualize the surveying problem from the textbook. The goal is a professional-quality technical schematic that is easy to understand.

**1. Scene Layout and Ground Levels:**
*   On the far right side of the plot, draw a tall, vertical grey line for the chimney.
*   To the left of the chimney, draw two ground station points, P and R. P should be closer to the chimney than R.
*   Draw the ground level for station P as a horizontal brown line.
*   Draw the ground level for station R as a separate, lower horizontal brown line to clearly show they are at different elevations.

**2. Stations, Instruments, and Vane:**
*   **At Station R:**
    *   Label the ground point 'R'.
    *   From R, draw a short vertical line up to the instrument axis. Label this point 'R''. Label the height `ht(R) = 1.64 m`.
    *   **Crucially, draw a horizontal dashed black line that ORIGINATES at R' and extends to the right.** This is the horizontal reference line for station R.
*   **At Station P:**
    *   Label the ground point 'P'.
    *   From P, draw a vertical purple line upwards.
    *   On this purple line, mark the instrument axis at 1.87 m above P. Label this point 'P''. Label the height `ht(P) = 1.87 m`.
    *   On the same purple line, mark the vane at 2.0 m above P. Label this point 'V'. Label the height `r = 2.0 m`.
    *   **Crucially, draw a separate, higher horizontal dashed black line that ORIGINATES at P' and extends to the right.** This is the horizontal reference line for station P.

**3. Lines of Sight (use distinct, solid colors):**
*   Draw a solid **red** line from P' to the top of the chimney, Q.
*   Draw a solid **blue** line from R' to the top of the chimney, Q.
*   Draw a solid **orange** line from R' to the vane, V.
*   Label the top of the chimney 'Q' and its base 'F'.

**4. Annotations, Dimensions, and Angles:**
*   **Horizontal Distances:**
    *   Indicate the horizontal distance between R and P with a double-arrowed line below the ground. Label it `b = 127 m`.
    *   Indicate the horizontal distance between P and the chimney's base F. Label it `D`.
*   **Vertical Distances (from solution):**
    *   Indicate the vertical distance between the two dashed horizontal lines (the difference in instrument heights). Label this `s = 34.34 m`.
    *   Indicate the vertical distance between the horizontal line from R' and the point V. Label this `h = 34.47 m`.
*   **Angles (use clear, curved arcs):**
    *   **At P':** Show the angle between the red line (P'Q) and the horizontal dashed line from P'. Label this `α₁ = 38° 21'`.
    *   **At R':**
        *   Show the angle between the orange line (R'V) and the horizontal dashed line from R'. Label this `α = 15° 11'`.
        *   Show the angle between the blue line (R'Q) and the horizontal dashed line from R'. Label this `α₂ = 21° 18'`. Ensure this arc is larger than the one for angle α.

**5. Final Polish:**
*   Add a title to the plot: "Surveying Problem Visualization".
*   Ensure all labels are placed clearly and do not overlap. Use a font size that is easy to read.
*   Turn off the plot axes (the default x/y grid) for a cleaner look.