focal point

Examples of focal point in the following topics:

• Thin Lenses and Ray Tracing

  • A ray entering a diverging lens parallel to its axis seems to come from the focal point F.
  • A ray entering a converging lens through its focal point exits parallel to its axis.
  • (a) Parallel light rays entering a converging lens from the right cross at its focal point on the left.
  • Rays of light entering a converging lens parallel to its axis converge at its focal point F.
  • (Ray 2 lies on the axis of the lens. ) The distance from the center of the lens to the focal point is the lens's focal length f.

• Introduction to Hyperbolas

  • The set of all points such that the difference between the distances to two focal points is constant
  • Then the difference of distances between $P$ and the two focal points is:
  • Thus, the standard form of the equation for a hyperbola with focal points on the $x$ axis is:
  • If the focal points are on the $y$-axis, the variables simply change places:
  • The ellipse can be defined as all points that have a constant sum of distances to two focal points, and the hyperbola is defined as all points that have constant difference of distances to two focal points.

• Image Formation by Spherical Mirrors: Reflection and Sign Conventions

  • Before that can be done, the focal point must first be defined.
  • The distance to the focal point from the mirror is called the focal length.
  • In this case, the focal point is behind the mirror.
  • A convex mirror has a negative focal length because of this.
  • The focal point is the same distance from the mirror as in a concave mirror.

• The Thin Lens Equation and Magnification

  • A ray entering a converging lens parallel to its axis passes through the focal point F of the lens on the other side.
  • A ray entering a diverging lens parallel to its axis seems to come from the focal point F.
  • A ray entering a converging lens through its focal point exits parallel to its axis.
  • A ray that enters a diverging lens by heading toward the focal point on the opposite side exits parallel to the axis.
  • The first ray is one that enters the lens parallel to its axis and passes through the focal point on the other side (rule 1).

• Refraction Through Lenses

  • The point at which the rays cross is defined as the focal point F of the lens.
  • The distance from the center of the lens to its focal point is defined as the focal length f of the lens. shows how a converging lens, such as that in a magnifying glass, can concentrate (converge) the nearly parallel light rays from the sun towards a small spot.
  • In this case, the lens is shaped so that all light rays entering it parallel to its axis appear to originate from the same point F, defined as the focal point of a diverging lens.
  • The distance from the center of the lens to the focal point is again called the focal length f of the lens.
  • Light rays from the sun are nearly parallel and cross at the focal point of the lens.

• Parts of a Hyperbola

  • Therefore the focal points are located at $(h+2\sqrt{m},k+2\sqrt{m})$ and $(h-2\sqrt{m},k-2\sqrt{m})$.

• Parabolas As Conic Sections

  • The vertex is therefore also a point on the cone, and the distance between that point and the cone's central axis is the radius of a circle.
  • The focal length is the leg of the right triangle that exists along the axis of symmetry, and the focal point is the vertex of the right triangle.
  • Using the definition of sine as opposite over hypotenuse, we can find a formula for the focal length "$f$" in terms of the radius and the angle:
  • The vertex will be at the point:
  • A right triangle is formed from the focal point of the parabola.

• The Telescope

  • The objective lens (at point 1) and the eyepiece (point 2) gather more light than a human eye can collect by itself.
  • The image is focused at point 5, and the observer is shown a brighter, magnified virtual image at point 6.
  • This causes the parallel rays to converge at a focal point, and those that are not parallel converge on a focal plane.
  • The object being observed is reflected by a curved primary mirror onto the focal plane.
  • (The distance from the mirror to the focal plane is called the focal length. ) A sensor could be located here to record the image, or a secondary mirror could be added to redirect the light to an eyepiece.

• Combinations of Lenses

  • The simplest case is where lenses are placed in contact: if the lenses of focal lengths f1 and f2 are "thin", the combined focal length f of the lenses is given by
  • The distance from the second lens to the focal point of the combined lenses is called the back focal length (BFL).
  • If the separation distance is equal to the sum of the focal lengths (d = f1+f2), the combined focal length and BFL are infinite.
  • The magnification can be found by dividing the focal length of the objective lens by the focal length of the eyepiece.
  • Calculate focal length for a compound lens from the focal lengths of simple lenses

• The Lensmaker's Equation

  • The beam after passing through the lens appears to be emanating from a particular point on the axis in front of the lens; the distance from this point to the lens is also known as the focal length, although it is negative with respect to the focal length of a converging lens.
  • The focal length of a thick lens in air can be calculated from the lensmaker's equation:
  • The focal length f is positive for converging lenses, and negative for diverging lenses.
  • The reciprocal of the focal length, 1/f, is the optical of the lens.
  • If the focal length is in meters, this gives the optical power in diopters (inverse meters).