Geometric optics is a branch of optics that focuses on the study of light as rays, without considering its wave nature. It deals with the behavior of light when it interacts with surfaces and boundaries, particularly in terms of reflection and refraction. Geometric optics is primarily concerned with the formation of images by optical elements such as lenses and mirrors and the principles governing their behavior.

In this article, we will learn in detail about geometric optics, optical instruments based on geometric optics, formulas and examples.

What is Geometric Optics?

Geometric optics is the study of light propagation in terms of rays, disregarding its wave nature, to understand how light interacts with surfaces and objects. It provides a simplified framework for analyzing optical systems, making predictions about image formation, and designing devices like lenses and mirrors.

Fundamental Principles of Geometric Optics

In geometric optics, there are two basic rules:

• First, light moves in straight lines when it travels through something even like air or water.
• Second, if light goes back through the same stuff it came from, it goes back along the same path it took before.

Laws of Geometric Optics

There are two basic laws that we study in geometric optics

• The optics’ law of reflection which states that the angle of incidence is equal to the angle of reflection when light strikes a surface.
• Another law of optics which explains how light bends when passing through two different media is the law of refraction. The bending act differently through different refractive indices of the media.

Law of Reflection

The law of reflection is asserted by reflecting light rays. It states that

• The angle of the incident equals the angle of the reflected measured along the same angle with respect to the surface at the point of incidence.
• The incident ray, reflected ray and normal which is an imaginary line, all lie in the same plane

Check, Reflection of Light

Law of Refraction or Snell’s Law

According to Snell’s Law, which is also often referred to as the Law of Refraction, light beams experience deviation when they travel from one medium through another medium. This phenomena is called refraction of light. It tells that the ratio between the sine of the incident angle to the sine of the refraction angle is a constant for particular pairs of two media unless the medium in the medium is changed.

Mirrors in Geometric Optics

In geometric optics, mirrors are essential components that play a crucial role in reflecting light rays. They come in two primary types: concave mirrors and convex mirrors. There are two types of mirrors we have to study in geometric optics

• Plane Mirrors
• Spherical Mirrors

Plane Mirrors

• Plane mirror is a flat reflecting surface.
• When light from the source strikes a plane mirror, we observe that the light is reflected at an angle equal to the incident angle.
• Any object for instance will be seen as flipped with respect to left and right in the reflected image through the plane mirror.
• In the plane mirror the factors like size and distance of the reflection take the values just the same as the object’s.
• You may use flat mirrors like the ones in home or car mirrors as well as in periscopes. Similarly, you can undertake lots of science experiments that use flat mirrors.
• Unlike the rest of the mirrors, plane mirrors don’t tend to either enlarge or, on the contrary, shrink the objects.

Spherical Mirror

• Spherical mirrors have a rounded reflective surface, either curving inward (concave) or outward (convex).
• They’re used in optical gadgets like telescopes, microscopes, and makeup mirrors.
• The focal length of a spherical mirror is half its radius of curvature.
• Sometimes, spherical aberration occurs, causing image distortion away from the center.
• The center of curvature is where the mirror’s curve would continue to form a full sphere, and the focal point is halfway between this center and the mirror.
• Diagrams with rays are often used to understand how light behaves when reflected by spherical mirrors.

Spherical mirrors are of two types

• Concave Mirror
• Convex Mirror

Concave Mirrors

• Concave mirrors are a kind of curvature where the surface is curved inward, like the inner surface of a sphere.
• The rays of light in this phenomenon are reflected in mirrors with a reflective surface that bulges inward, as the result it causes parallel light rays to converge at a focal point after reflection.
• Concave mirrors are mainly used in applications that require focusing light, like in a telescope, the mirror used for shaving, and the automobile headlights.
• The image formed by a concave mirror could be either virtual or real depending on how adjacent to its focus the object is positioned.

Convex Mirrors

• The shape of a convex mirror is an arc, and looks like a ball rising upwards.
• They deflect light at the angle described by the law of reflection
• Concave mirrors are commonly applied to systems having a wide field of view which includes: rearview mirrors in vehicles, surveillance cameras or even decorative mirrors.
• Virtual (virtual), diminished, and erect images, which are the types of images produced by convex mirrors

Learn, Concave and Convex Mirrors

Lenses in Geometric Optics

In geometric optics, lenses are optical devices designed to refract (bend) and focus light rays to form an image. There are two primary types of lenses: convex and concave.

Convex Lens

• Convex lens are known as converging lens.
• Thicker in the middle and thinner at the edges.
• Converges parallel incident rays to a focal point on the opposite side of the lens.
• Forms real, inverted images if the object is located beyond the focal point, and virtual, upright images if the object is within the focal point.

Concave Lens

• Concave lens are known as diverging lens.
• Thinner in the middle and thicker at the edges.
• Diverges parallel incident rays, making them appear to originate from a focal point on the same side of the lens.
• Forms virtual, upright, and reduced images.

Ray Tracing in Geometric Optics

Ray tracing is a technique of geometry that is being applied with its differential properties in the field of optics to trace the path a light takes while interacting with different optical elements. It is concerned with movements of light rays along optical system where the essential picture properties, reflection, refraction, and dispersion, can be predicted. 

It is a fundamental technique that is used in the optical system design and analysis while making prisms, mirrors, and lenses to ensure their behavior in the varying circumstances. By using ray tracing, engineers and scientists are able to understand the properties of their optical systems and guarantee that the created ones meet the set specifications.

Learn more about Ray Tracing

• Image Formation by Spherical Mirror 
• Image formation by Lenses

Optical Instruments in Geometric Optics

Optical instruments in geometric optics play pivotal roles in various fields, offering precise visualization and manipulation of light for different applications.

Microscopes

Microscopes utilize lenses to magnify small objects, enabling detailed examination of microscopic structures in fields such as biology, medicine, and materials science.

Telescopes

Telescopes are designed to gather and focus distant light, facilitating the observation of celestial objects like stars, planets, and galaxies. They come in various types, including refracting and reflecting telescopes, each with its own advantages for astronomical research.

Cameras

Cameras capture images by focusing light onto a photosensitive surface, such as film or a digital sensor. They are widely used in photography, videography, surveillance, and scientific imaging.

Projectors

Projectors project images or videos onto screens or surfaces using light beams. They find applications in presentations, entertainment, education, and simulation, among others.

Refraction Through Glass Slab

When light travels from one medium to another, like air to glass, it changes direction, called refraction. A glass slab, like a rectangular piece of glass, demonstrates this. When light enters the slab, it bends towards the normal (an imaginary line perpendicular to the surface). Inside, it continues in a straight line unless it exits the slab, where it bends away from the normal. This bending causes objects viewed through the slab to appear shifted. The degree of shift depends on the angle of incidence and the refractive index of the glass. This phenomenon finds applications in lenses, prisms, and optical instruments.

Learn More, Refraction of Light through Glass Slab

Refractive Index

Refractive index is a basic characteristic of material that characterizes light travelling through it. It is the speed of light in a vacuum being divided by the speed of light in the material. When a light wave moves from one medium to another with different refractive index its speed and direction are changed and this causes light refraction. Different materials have got different refractive indexes, which are as well affected by the factors including wavelength, temperature, and pressure.

The formula of refractive index is given as

n = c/v

where,

• n is refractive index of the medium
• c is speed of light
• v is velocity of light in that medium

Geometric Optics Formula

The following table contains all the formulas used in geometric optics