Is the magnification in a convex lens positive?

Lenses and magnifying glasses

In experiments on optics, these two things are often used to bundle, focus or deflect light rays. For this reason, we would like to introduce these important devices in more detail here.

A lens consists of two surfaces that can refract light. These are either both concave or both convexly curved or one surface each is concave or convexly curved. Probably the most important size of a lens is its focal length.
In most cases a lens is circular and its free area, which is needed to change the light, is called the aperture. In addition to the aperture and the focal length, the radius of curvature of a lens also plays a role. If the center of curvature of a surface is to the right of the optical center of the lens, then one speaks of a positive radius of curvature, and if the center of curvature is to the left, of a negative.
A distinction is now made between different types of lenses, depending on their shape:
  • Collecting lenses: Collecting lenses have at least one convex surface. This means that the surface is curved outwards. Another characteristic of collecting lenses is that they vary in thickness. In the middle (at the optical axis) these lenses are thicker than at the edge. There are three types of converging lenses:
    1. biconvex lenses: here both surfaces are convexly curved.
    2. Plano-convex lenses: one surface is convex, the other is planar (such flat surfaces have an infinite radius of curvature).
    3. Concave-convex lenses: The name comes from the more curved surface. In this case, the concave curvature is greater than the convex.
    If you want to describe the surfaces with the help of the radius of curvature, a converging lens has a positive radius of curvature on the side of the incident light and a negative one on the side of the emerging light.
    As the name suggests, the incident light is collected on the other side of the lens in the focal point. The rays of light falling parallel to the optical axis are refracted in such a way that they pass through the focal point of a lens. The distance between the focal point and the center of the lens is also known as the focal length. Since the focal length of a lens depends on the strength of the curvature (the greater the curvature, the shorter the focal length), a biconvex lens with the same radius of curvature as a plano-convex lens still has a shorter focal length.
  • Diverging lenses: In contrast to the collective lenses, the diverging lenses have at least one concave, i.e. inwardly curved, surface. With them the radius of curvature is negative on the side of the incident light and positive on the side of the exiting light. Here, too, a distinction is made between three types of diffusing lenses:
    1. biconcave lenses: here both surfaces are concave.
    2. Plano-concave lenses: one surface is concave, the other is planar.
    3. Convex-concave lenses: In contrast to the concave-convex lens mentioned above, the convex curvature here is significantly stronger than the concave.
    In addition, concave lenses are thinner in the center, near the optical axis, than at the edge.
    In the case of the diverging lenses, the incident light rays diverge on the other side. This means that the extensions of the rays meet in the apparent focus (this is on the side of the incident light).

Fig. 942 Lens defect (SVG)

Fig. 938 Beam path with a concave mirror and with a concave lens (SVG)
With lenses, however, you have to be aware that imaging errors can occur. This is due, on the one hand, to the fact that marginal rays do not necessarily have the same focal point as the rays extending further inside and, on the other hand, to the thickness of the lenses.
The following can be said about the images of converging lenses:
If the object is outside of twice the focal length, the resulting image is smaller, real, but also vice versa.
If the object is between the double focal length and the single focal length, the image is enlarged, reversed and real.
If the object is within the focal length (as with the magnifying glass), the image is enlarged, upright, but virtual.

The lens equation
This is used to determine the image of an ideal lens. The lens equation has the following form:

in which is the focal length of the lens, the so-called object distance, i.e. the distance between the object and the optical center of the lens and the image distance (the distance between the image and the optical center of the lens). Do you know the magnification of the system, the image distance or the object distance can be determined with the help of the focal length. Furthermore applies to the size of the object and the picture the following relationship:

If the lens equation for a system is fulfilled, the image of the object can be seen clearly.
In order to adjust the optical setups as well as possible in the individual experiments, one should pay attention to the focal lengths of the lenses and make clear what kind of lenses it is and what the path of the light rays in the system looks like.

Magnifying glass
A magnifying glass is a convex lens that has a small focal length. A virtual enlarged image is generated of the viewed object if it is within the focal length. Parallel light is directed into the eye through the magnifying glass. With the help of a magnifying glass you can also determine the magnification of an object. For this you need the viewing angle :

and receives for enlargement :

in which the viewing angle is without a magnifying glass and the reference viewing distance. For the human eye, this is 25 cm.