Shining a torch

Manipulate[
 Show[RegionPlot3D[\[Sqrt](x^2 + y^2) <=
     z && (z Cos[\[Theta]] - x  Sin[\[Theta]] >
      2 Cos[\[Theta]]), {x, -10, 10}, {y, -10, 10}, {z, -2, 10},
   Mesh -> None, PerformanceGoal -> "Quality", PlotPoints -> 20,
   PlotStyle -> White, Lighting -> "Neutral", Axes -> None,
   Boxed -> False, ViewPoint -> {0.2, 0.2, -5}],
  RegionPlot3D[ (z Cos[\[Theta]] - x  Sin[\[Theta]] >
     2.1 Cos[\[Theta]]), {x, -10, 10}, {y, -10, 10}, {z, -2, 10},
   Mesh -> None, PerformanceGoal -> "Quality", PlotPoints -> 20,
   PlotStyle -> GrayLevel[0.1]]
  , Graphics3D[
   {Red, Cylinder[{{0, 0, 0}, {0, 0, -0.5}}, 0.5], Blue,
    Cylinder[{{0, 0, 0}, {0, 0, -2}}, 0.3]}
   ]
  , ImageSize -> {240}],
 {{\[Theta], Pi/3}, 0, Pi/2}]