lens

Examples of lens in the following topics:

• The Lensmaker's Equation

  • A lens whose thickness is not negligible is called a thick lens.
  • If the lens is biconvex, a beam of light travelling parallel to the lens axis and passing through the lens will be converged (or focused) to a spot on the axis, at a certain distance behind the lens (i.e. the focal length).
  • In this case, the lens is called a positive or converging lens.
  • If the lens is biconcave, a beam of light passing through the lens is diverged (spread); the lens is thus called a negative or diverging lens.
  • Diagram of a negative (diverging) lens.

• The Compound Microscope

  • It is made of two convex lenses: the first, the ocular lens, is close to the eye; the second is the objective lens.
  • The first lens is called the objective lens and is closest to the object being observed.
  • The objective lens creates an enlarged image of the object, which then acts as the object for the second lens.
  • The distance between the objective lens and the ocular lens is slightly shorter than the focal length of the ocular lens, fe.
  • where m is total magnification, mo is objective lens magnification, me is ocular lens magnification.

• Refraction Through Lenses

  • Such a lens is called a converging (or convex) lens for the corresponding effect it has on light rays.
  • The concave lens is a diverging lens, because it causes the light rays to bend away (diverge) from its axis.
  • The distance from the center of the lens to the focal point is again called the focal length f of the lens.
  • The more powerful the lens, the closer to the lens the rays will cross.
  • Compare the effect of a convex lens and a concave lens on the light rays

• Thin Lenses and Ray Tracing

  • An ideal thin lens has two refracting surfaces but the lens is thin enough toassume that light rays bend only once.
  • Another way of saying this is that the lens thickness is much much smaller than the focal length of the lens.
  • A thin symmetrical lens has two focal points, one on either side and both at the same distance from the lens.
  • The treatment of a lens as a thin lens is known as the "thin lens approximation. "
  • (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.

• The Thin Lens Equation and Magnification

  • How does a lens form an image of an object?
  • A ray entering a converging lens parallel to its axis passes through the focal point F of the lens on the other side.
  • The third ray passes through the nearer focal point on its way into the lens and leaves the lens parallel to its axis (rule 4).
  • The thin lens equation is:
  • Ray tracing is used to locate the image formed by a lens.

• Aberrations

  • An aberration is the failure of rays to converge at one focus because of limitations or defects in a lens or mirror.
  • This aberration happens when the lens fails to focus all the colors on the same convergence point .
  • Since violet rays have a higher refractive index than red, they are bent more and focused closed to the lens. shows a two-lens system using a diverging lens to partially correct for this, but it is nearly impossible to do so completely.
  • Spherical aberrations are a form of aberration where rays converging from the outer edges of a lens converge to a focus closer to the lens, and rays closer to the axis focus further.
  • The apparent effect is that of an image which has been mapped around a sphere, like in a fisheye lens.

• Combinations of Lenses

  • A compound lens is an array of simple lenses with a common axis.
  • In contrast to a simple lens, which consists of only one optical element, a compound lens is an array of simple lenses (elements) with a common axis.
  • An achromatic lens or achromat is a lens that is designed to limit the effects of chromatic and spherical aberration.
  • In the most common type (shown in ), the positive power of the crown lens element is not quite equaled by the negative power of the flint lens element.
  • Calculate focal length for a compound lens from the focal lengths of simple lenses

• The Magnifying Glass

  • A magnifying glass is a convex lens that lets the observer see a larger image of the object being observed.
  • A magnifying glass is a convex lens that lets the observer see a larger image of the object under observation.
  • The lens is usually mounted in a frame with a handle, as shown below .
  • The highest magnifying power is obtained by putting the lens very close to the eye and moving both the eye and the lens together to obtain the best focus.
  • When the lens is used this way, the magnifying power can be found with the following equation:

• Newton's Rings

  • The outer rings are spaced more closely than the inner ones because the slope of the curved lens surface increases outwards.
  • where N is the bright-ring number, R is the radius of curvature of the lens the light is passing through, and λ is the wavelength of the light passing through the glass.
  • A spherical lens is placed on top of a flat glass surface.
  • An incident ray of light passes through the curved lens until it comes to the glass-air boundary, at which point it passes from a region of higher refractive index n (the glass) to a region of lower n (air).
  • As one gets farther from the point at which the two surfaces touch, the distance d increases because the lens is curving away from the flat surface .

• The Human Eye

  • The lens of the eye is similar to one in glasses or cameras.
  • The lens provides the remaining power.
  • The image passes through several layers of the eye, but happens in a way very similar to that of a convex lens.
  • The power of the lens of an eye is adjustable to provide an image on the retina for varying object distances.
  • Layers of tissues with varying indices of refraction in the lens are shown here.