concave

Examples of concave in the following topics:

• Image Formation by Spherical Mirrors: Reflection and Sign Conventions

  • Spherical mirrors can be either concave or convex.
  • A summary of the properties of concave mirrors is shown below:
  • The focal point is the same distance from the mirror as in a concave mirror.
  • This figure shows the difference between a concave and convex mirror.
  • This is a ray diagram of a concave mirror.

• Refraction Through Lenses

  • shows the effect of a concave lens on rays of light entering it parallel to its axis (the path taken by ray 2 in the figure is the axis of the lens).
  • The concave lens is a diverging lens, because it causes the light rays to bend away (diverge) from its axis.
  • Compare the effect of a convex lens and a concave lens on the light rays

• The Lensmaker's Equation

  • The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave.
  • The sign convention used to represent this varies, but for our treatment if R1 is positive the first surface is convex, and if R1 is negative the surface is concave.
  • The signs are reversed for the back surface of the lens: if R2 is positive the surface is concave, and if R2 is negative the surface is convex.

• Stability, Balance, and Center of Mass

  • Explicitly, if the potential is concave-up at x0, $\left.
  • \frac{d^2 U(x)} {dx^2} \right|_{x_0} > 0$, then the system is stable; conversely, if the potential is concave-down, then the equilibrium is unstable.
  • If the ball is at the top of the hill (where the potential is concave-down) it is possible for it to be perfectly balanced, and therefore at equilibrium .

• Combinations of Lenses

  • A convex plus a concave lens (f1 > 0 >f2) produces a positive magnification and the image is upright.
  • The most common type of achromat is the achromatic doublet, which is composed of two individual lenses made from glasses with different amounts of dispersion Typically, one element is a negative (concave) element made out of flint, which has relatively high dispersion, and the other is a positive (convex) element made of crown glass, which has lower dispersion.

• Thin Lenses and Ray Tracing

  • Shows how to draw the ray diagrams for locating the image produced by a concave lens and a convex mirror.

• Satellites

  • Additionally the Moon's orbit with respect to the Sun is always concave.

• Non-relativistic Shocks

  • Because all of the adiabats are concave up in the $p-V-$plane, the slope of the secant must be larger than that of the tangent at $(p_1,V_1)$, so the flow enters the shock supersonically.