thin lens

Examples of thin lens in the following topics:

• The Thin Lens Equation and Magnification

  • The thin lens equation relates the object distance do, image distance di, and focal length f.
  • The thin lens equation is:
  • In many cases both of these equations are referred to together as the thin lens equations.
  • The thin lens equations are broadly applicable to all situations involving thin lenses (and "thin" mirrors).
  • Shows how to use the thin lens equation to calculate the image distance, image height and image orientation for convex lenses when the object distance is greater the the focal length (f).

• Thin Lenses and Ray Tracing

  • A thin lens is defined to be one whose thickness allows rays to refract, as illustrated in , but does not allow properties such as dispersion and aberrations.
  • An ideal thin lens has two refracting surfaces but the lens is thin enough toassume that light rays bend only once.
  • 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. "
  • Describe properties of a thin lens and the purpose of ray tracing

• The Lensmaker's Equation

  • Unlike idealized thin lenses, real lenses have a finite thickness between their two surfaces of curvature.
  • An ideal thin lens with two surfaces of equal curvature would have zero optical power, meaning that it would neither converge nor diverge light.
  • A lens whose thickness is not negligible is called a thick 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.
  • In this case, the thin lens approximation can then be made and the lensmaker's equation can be approximated as

• 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
  • Since 1/f is the power of a lens, it can be seen that the powers of thin lenses in contact are additive.
  • If two thin lenses are separated in air by some distance d (where d is smaller than the focal length of the first lens), the focal length for the combined system is given by
  • As d tends to zero, the value of the BFL tends to the value of f given for thin lenses in contact.
  • An achromatic lens or achromat is a lens that is designed to limit the effects of chromatic and spherical aberration.

• 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

• 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.

• 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 .

• Thin Film Interference

  • Thin film interference occurs when incident light waves reflected by the different layers of a thin film interfere and form a new wave.
  • The thickness of a thin film is a few times smaller than the wavelength of the light, λ.
  • The colors that appear in bubbles that kids play with are also a result of thin film interference.
  • shows a diagram of how thin film interference works.
  • Light incident on a thin film.