Nepedia
Back to Discover
Advanced Reader
⚛️

Geometrical optics

physical science Maturity 7-9 Next article →

Geometrical optics, often called ray optics, is a scientific model used to describe how light travels. Instead of looking at light as a complex wave, this model treats light as thin lines called rays.

Plane wave wavefronts 3D
Plane wave wavefronts 3D

These rays are abstractions that help scientists approximate the paths light takes. A ray is technically a line perpendicular to light's wavefronts. This model is extremely useful when the wavelength of light is small compared to the objects it hits. It allows us to study the geometry of imaging and understand optical aberrations, which are distortions in an image.

Light rays follow very specific rules as they move through different environments. In a homogeneous medium, which is a material that is the same throughout, light travels in straight lines. However, rays can bend when they hit the interface between two different media. They can also follow curved paths if the refractive index of the medium changes gradually. A ray might also be absorbed by a material or reflected off a surface. Fermat's principle provides a rigorous way to define these paths. It states that a ray takes the path that requires the least amount of time to travel between two points.

Reflection is one of the most common ways light interacts with surfaces. When light hits a glossy surface like a mirror, it reflects in a predictable way. This follows the Law of Reflection. To understand this, imagine a line called the surface normal, which is perpendicular to the mirror at the point of impact. The angle between the incoming incident ray and the normal is equal to the angle between the reflected ray and the normal. The incident and reflected rays always stay within a single plane.

Reflection angles
Reflection angles

This process can create real images or virtual images, which are images that appear to be in a specific location in space.

Mirrors can be flat or curved, and they behave quite differently. A flat mirror produces an image that is upright and the same size as the object. The magnification of a flat mirror is exactly one. These images are also parity inverted, meaning they show a left-right reversal. Curved mirrors, however, can change the size and orientation of an image. A parabolic mirror can take parallel rays and make them converge at a single common focus.

Spherical mirrors can cause spherical aberration, which smears the focus. Curved mirrors can create upright virtual images or inverted real images that can be projected onto a screen.

Refraction is the process where light bends as it moves between different materials. This happens because the speed of light changes depending on the medium's index of refraction. When light moves from one medium to another, its path is described by Snell's Law.

Snells law
Snells law

This law relates the angles of the incident and refracted rays to the refractive indices of the two materials. For example, if light moves from a material with a high index to one with a low index, it might experience total internal reflection. This means no light is transmitted through the interface. This specific phenomenon is what allows fiber optic technology to work by carrying light signals through cables with almost no loss.

Lenses are devices designed to produce converging or diverging light rays through refraction. There are two main types: convex and concave lenses. Convex lenses are thicker in the middle and cause parallel rays to converge toward a focal point.

Lens3b
Lens3b

Concave lenses are thinner in the middle and cause rays to diverge, or spread apart.

2015-05-25 0836With concave lenses, incoming parallel rays diverge after going through the lens, in such a way that they seem to have originated at an
2015-05-25 0836With concave lenses, incoming parallel rays diverge after going through the lens, in such a way that they seem to have originated at an

Scientists use the lensmaker's equation and the thin lens equation to predict where images will form. These mathematical tools help determine the object distance, image distance, and focal length.

History and advanced mathematics help us refine these optical models. Isaac Newton famously used a prism to demonstrate that refraction can create a dispersion spectrum, which looks like a rainbow. This happens because different frequencies of light have slightly different refractive indices. Today, we use gradient-index (GRIN) materials, where the refractive index changes gradually. This is used in modern scanners and photocopiers. Mathematically, geometrical optics emerges as a short-wavelength limit of more complex equations. It remains a vital tool for understanding how we see and how we build technology to capture light.

707 words

Where will your curiosity go next?

Keep exploring at your chosen reading level.

🖼️ Images & Media (7)
File:Snells law.svg
Snells law.svg
File:Lens3b.svg
Lens3b.svg
File:Plane wave wavefronts 3D.svg
Plane wave wavefronts 3D.svg
File:Reflection angles.svg
Reflection angles.svg
File:2015-05-25 0820Incoming parallel rays are focused by a convex lens into an inverted real image one focal length from the lens, on the far side of the.png
2015-05-25 0820Incoming parallel rays are...
File:2015-05-25 0836With concave lenses, incoming parallel rays diverge after going through the lens, in such a way that they seem to have originated at an.png
2015-05-25 0836With concave lenses,...
File:Virtualimageframerate1.gif
Virtualimageframerate1.gif
More to explore

🔗 What's this?

Concepts mentioned in this article

🪜 Step back

Simpler topics to build understanding

What is Nepedia?

A free, ad-free encyclopedia for children. Every article is written at five reading levels, so the same page works for a five-year-old and a fifteen-year-old — use the level switcher above to see this one change. No account needed to read.