The lens in physics. Characteristics and application

A lens is a simple optical device that consists of one or more blocks of transparent material (usually glass, but also plastics, minerals, gels, paraffin) glued together. Most often it occurs in the shape of a cylinder sector, and in the place of bases it is limited by spherical surfaces. What are the types of lenses? What is their use?

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1. What is a lens?

The lens is usually made of glass, but not always. It is transparent, the material from which it is made has a different light refraction index than the medium in which it is located. More precisely, the point here is for the wave in front of the lens to change its direction after entering it.

Speaking of the lens, we are not only dealing with light, therefore we should use the universal concept of wave refraction, not light; there may also be acoustic lenses designed to refract sound waves.

Usually, during our education, we learn about glass lenses, but they can be made of solid, liquid or gaseous bodies.

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2. Types of lenses

Lenses are divided according to their focusing ability. According to this criterion, we can distinguish lenses:

  • focusing;
  • distracting.

Another criterion for classifying lenses is their design. In this division, we distinguish lenses:

  • single (e.g. glasses in glasses);
  • complex (e.g. Fresnel lens used in lighthouses).

The most common division of lenses, however, is according to their shape. According to this criterion, we distinguish lenses:

  • biconcave;
  • biconvex;
  • flat - convex;
  • flat - concave;
  • concave - convex.

3. Properties of the lens

Each lens has a point called a focal point and an optical axis. It is limited by spherical surfaces which are spherical segments, and the centers of the spheres define a straight line which is the optical axis of the lens.

The focal length of the lens is marked with the letter F, it is the point on the optical axis of the lens where the directions of the waves or their extensions intersect.


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We write the mathematical description of a thin lens with the formula:

1f = 1x + 1y = (n2n1−1) (1r1 + 1r2)

Considering that the angle between the axis of the lens and the rays of the waves is not large, and that:

  • f is the focal distance from the lens;
  • n1 is the refractive index of the medium in which the lens is located;
  • n2 is the refractive index of the lens;
  • r1 and r2 are the radii of the spherical surfaces of the lens;
  • x is the distance of the object from the lens;
  • y is the image distance from the lens.

For the radii of spherical surfaces, we assume a negative sign for concave surfaces and a positive sign for convex surfaces. For planar r = ∞ and for 1r = 1∞ = 0.

The focal distance from the lens is negative for scattering lenses and positive for focusing lenses.

It is worth bearing in mind that the mathematical description shows a thin lens which, in a simplified way, represents reality.

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4. Use of lenses

Lenses are used in many optical instruments for shaping a light beam or creating an image. They are placed in:

  • film cameras;
  • cameras;
  • lunettes;
  • microscopes;
  • binoculars;
  • magnifiers;
  • medicated glasses;
  • eye contact lenses;
  • spectrophotometers;
  • lenticular printing;
  • light railroad semaphores.
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