Concave or diverging lenses

Geometrical optics of concave or diverging lenses

Geometrical optics is the part of optics that deals, based on geometrical representations, with the changes of direction that luminous rays undergo in the various phenomena of reflection and refraction.

Geometrical optics is based on the following assumptions:

– Light propagates rectilinearly

– Light rays are reversible. The path followed by a ray is independent of whether it is in one direction or in the opposite direction.

– The laws of reflection and refraction are fulfilled.

With these simple fundamentals we can determine the passage of light through the various optical instruments, as in this case the concave lenses, and the shape, size and position of the images obtained by means of them.

The geometrical optics of a concave lens can be explained by applying the laws of reflection and refraction of light. Ray tracing is the technique for determining or following the paths that light rays follow. Ray tracing for optical lenses is very similar to the technique used with mirrors.

A concave lens diverges incident rays parallel to the axis in a diverging manner. The rays diverge as they leave the lens, and appear to come from a point on the same side of the lens as the object. This optical property is due to the inward curved surface of the lens causing light to refract outward. Concave lenses form virtual, reduced, non-inverted images.

The rules governing the paths of light rays in a concave (or diverging) lens are:

1. A ray entering a concave (or diverging) lens parallel to the optical axis is refracted in such a way that it appears to diverge from a virtual focal point on the same side of the lens as the incident ray.
2. A ray passing through the center of a concave (or diverging) lens is not deflected.
3. A ray approaching along the line passing through the focal point of a concave (or diverging) lens exits on the opposite side of the lens parallel to the axis.

Imaging in a concave or diverging lens

Similarly, imaging with a concave lens can be analyzed using the ray tracing technique to determine the different types of images that can be created. We also developed equations to quantitatively analyze the properties of concave lenses.

When an object is placed in front of a concave lens, image formation follows certain principles:

1. If the object is placed in any position in front of the concave lens, the image formed will be virtual, right, i.e. oriented in the same direction as the object, and smaller than the object.
2. This virtual image is formed on the same side of the lens as the object, at a distance smaller than the distance from the object to the lens.

The mathematical relationship describing image formation in concave lenses is the lens equation:

1/f = 1/u+ 1/v

Where:

f focal length

u distance from object to lens

v distance from the image to the lens

In some circumstances, a lens forms a real image, as when a movie projector projects an image onto a screen. In other cases, the image is a virtual image, which cannot be projected on a screen. Where, for example, is the image formed by the eyeglasses?

Let’s look at the following example. Suppose we have a concave lens with a focal length of -10 cm, and an object placed 30 cm from the lens. Using the lens equation:

1/(-10) = 1/30+ 1/v

From this equation we obtain:

v = -15 cm

This means that the image is formed at 15 cm on the same side of the lens as the object, it is virtual and smaller.

Study with these simulations here and here how is the image formation how is the image formation with concave lenses.

Applications of concave or diverging lenses

These lenses are commonly used in the manufacture of eyeglasses, telescopes and other optical devices.

In the case of eyeglasses, concave lenses are used to correct myopia. Nearsightedness is a condition in which a person can see near objects clearly, but has difficulty seeing distant objects. Concave lenses help correct this condition by scattering the light entering the eye, allowing the image to focus on the retina.

In telescope manufacturing, concave lenses are used in the objectives of reflecting telescopes. In these telescopes, a concave lens is placed at the front of the telescope tube and reflects the incoming light onto a concave mirror at the rear of the tube. The concave mirror reflects the light into an eyepiece, where the image is focused for viewing.

Concave lenses are also used in the manufacture of microscopes, cameras and other optical instruments.