Thin optical Lenses. Geometrical optics, thickness and curvature

Geometrical optics

Geometrical optics is the part of optics that deals, based on geometrical representations, with the changes of direction that light rays undergo in the different 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.

Types of thin optical lenses

Thin lenses can be of two main types:

Convex or converging lenses. These lenses are thicker in the center than at the edges and cause the light rays passing through them to converge at one point, known as the focus. Here is more detailed information about these types of lenses.

Concave or diverging lenses. These lenses are thinner in the center than at the edges and cause light rays passing through them to diverge as if coming from a focal point in front of the lens. Here is more detailed information about these types of lenses.

Parameters of thin optical lenses

The main parameters that characterize an optical lens are:

– Focus (F). The focus is the point where the rays parallel to the principal axis converge in a converging lens, or diverge in a diverging lens).

– Optical center (O). The optical center is the point of the lens through which light rays pass without deviation.

– Focal length (f). The focal length is the distance between the optical center of the lens and the focus.

Equations of thin optical lenses

The main equation for thin lenses relates the focal length of the lens to the object distance and the image distance and is expressed as:

1/f = 1/d0 + 1/di

Where

              f focal length

              do object distance

              di image distance

By convention, the distances of objects and images are considered to be positive if they are on the opposite side of the light source and negative if they are on the same side.

A crucial concept of a lens is magnification, i.e. the measure of how much the image of an object is enlarged or reduced as it passes through a lens. The magnification of a thin lens is defined as the ratio of the height of the image to the height of the object, and is directly related to the distances of the object and the image:

              M = hi/h0 = -di/d0

Where

              M magnification

ho object height

              hi image height

              do object distance

              di image distance

The values of M are to be interpreted as follows:

M positive The image is virtual and upright

M negative The image is real and inverted

Absolute value M > 1 The image is larger than the object.

Absolute value M < 1 The image is smaller than the object.

Example. Suppose an object of height ho forms an image of height hi. If the object distance d0 is 10 cm and the image distance di is -20cm (virtual image), applying the magnification equation we obtain that:

M = -di/d0 = – (-20)/10 =2

That is, the virtual image is right (same orientation as the object) and twice the size.

The magnification of a thin lens is a crucial concept in many optical devices (microscopes, telescopes, cameras, etc.) and its understanding is fundamental to the design and use of optical devices.

Design parameters of thin optical lenses

How can a lens be designed to perform the way we want it to? There are three basic design parameters that can be influenced: material, thickness and curvature.

Lens material determines basic characteristics such as transparency and refractive index.

The thickness of a lens refers to the distance between its two surfaces, measured along the centerline of the lens, and may be uniform or may vary across the lens, known as a lens of varying thickness.

The curvature of a lens refers to the shape of its surfaces, which may be concave (inward curvature) or convex (outward curvature), resulting in diverging and converging lenses, respectively. The curvature of a lens is measured in diopters (D) and is related to the ability of the lens to refract light. A more curved lens will have a greater refractive ability than a less curved lens.

The material, thickness and curvature of a thin optical lens are three of the most important characteristics that determine its optical behavior. These three parameters will determine the focus position and focal length and, ultimately, the behavior of the lens.

See in our simulations how changing these parameters of a lens produces different results. See what images different types of lenses produce, what happens when you modify the material (refractive index), thickness and curvature of a lens.

If you want to expand your knowledge about optical lenses visit our convex lenses and concave lenses pages.

Applications of thin optical lenses

Optical lenses have a very wide range of applications in various fields. Examples include eyeglasses, contact lenses and intraocular lenses; cameras and camcorders; microscopes, telescopes, periscopes and binoculars; projectors, displays and monitors; spectrometers and interferometers; automotive lamps, headlamps and lights; endoscopes and medical lasers; machine vision systems, bar code readers; augmented reality glasses and virtual reality helmets; fiber optics and optical measuring equipment.