An easy introduction to geometrical optics
Geometrical optics is the part of optics that treats light as straight-line rays and uses simple rules to predict what we see. It is the version of optics used in school ray diagrams, in basic camera and eyeglass design, and in everyday questions like: Why do mirrors show images? Why does a straw look bent in water? Why can a magnifying glass focus sunlight?
The whole subject rests on three ideas.
Light can be modeled as rays. In a uniform material such as still air or clear glass, those rays travel in straight lines.
At a surface, rays obey simple rules. They can reflect from the surface or refract, meaning bend as they enter a new material.
Mirrors and lenses form images by redirecting rays. Once you can track a few important rays, you can predict where an image appears and what it looks like.
A good way to think about geometrical optics is as a map, not the whole territory. Light also behaves like a wave, and that matters in some situations. But for many everyday optical systems, the ray model is simple, visual, and powerful.
The ray model of light
The ray model starts with a deliberate simplification: instead of describing light as a full electromagnetic wave, it treats light as if it moves along thin lines called rays. That is not the deepest description of light. It is the most useful first description for many problems.
A source is anything emitting light: the Sun, a lamp, a candle, a phone screen. From the source, rays spread outward. In a uniform medium—a material whose optical properties stay the same from place to place—those rays travel in straight lines. That straight-line travel is the reason shadows have sharp edges in ordinary situations and why line of sight matters.
The key ideas to hold onto
A ray shows the direction light travels.
A medium is the material light is moving through, such as air, water, or glass.
A shadow appears when an opaque object blocks rays from reaching some region.
Line of sight means you see an object when light from it can reach your eye.
Imagine a flashlight shining toward a wall with a book in the way. Rays that hit the book are blocked. Rays that go around it keep traveling. The dark region behind the book is the shadow. Nothing mysterious happened. Straight-line travel alone explains it.
The trap here is to think a ray is a tiny physical thread inside the light. It is better to think of a ray as a tracking line—a way of keeping account of where the light goes. Geometrical optics uses that tracking line because it works well for mirrors, lenses, and image formation on ordinary scales.
Reflection: how mirrors redirect light
Reflection happens when light hits a surface and bounces back into the original medium. For a smooth surface such as a mirror, the rule is precise: the angle of incidence equals the angle of reflection.
The important detail is how the angles are measured. They are not measured from the surface itself. They are measured from the normal, which is an imaginary line drawn perpendicular to the surface at the point where the ray hits. Beginners often mix this up. Measure from the normal, and the rule becomes easy to use.
Why a plane mirror image appears behind the mirror
Stand in front of a flat mirror. Rays from your face reflect from the mirror into your eyes. Your brain assumes light travels in straight lines, so it mentally extends those reflected rays backward. Those backward extensions seem to meet at a point behind the mirror. That apparent point is where the image seems to be.
This is why the image in a plane mirror is called a virtual image. The rays do not actually gather behind the mirror. They only appear to come from there.
A useful fact follows from the geometry: in a plane mirror, the image distance behind the mirror equals the object distance in front of the mirror. If you stand 1 meter in front of the mirror, your image appears 1 meter behind it. The image is also upright, though left and right appear swapped in an everyday sense.
A mirror does not put your image behind the glass. It sends rays to your eye in a pattern your brain interprets as coming from behind the glass.
Refraction: why light bends at a boundary
Refraction is the change in direction of light when it passes from one medium into another, such as from air into water or from air into glass. The reason is that light travels at different speeds in different materials.
The name for how strongly a material slows light is its refractive index. A higher refractive index means light travels more slowly there. You do not need the full equation yet. The beginner rule is enough:
When light enters a medium where it moves more slowly, it bends toward the normal.
When light enters a medium where it moves more quickly, it bends away from the normal.
A familiar example
Put a straw in a glass of water. The straw looks bent at the water surface. The straw itself is not bent. Light from the underwater part changes direction as it leaves the water and enters the air, so your eye traces those rays back to a shifted apparent position.
That is the pattern to remember: refraction changes where things appear to be.
The trap here is to think light bends because the surface “pushes” it sideways. It is better to think of one part of the wavefront changing speed before another part does, which changes the direction of travel. Geometrical optics compresses that deeper wave story into a ray rule: slower means toward the normal, faster means away.
Mirrors and lenses form images
Once reflection and refraction are in place, image formation becomes much easier to understand. Mirrors form images by reflecting rays. Lenses form images by refracting rays at their surfaces.
The big distinction is between real and virtual images.
A real image forms where rays actually meet. It can often be projected onto a screen.
A virtual image forms where rays only appear to come from. It cannot be projected onto a screen in the same direct way.[5]/24%3A_Geometric_Optics/24.3%3A_Lenses)
Converging and diverging
A system is converging if it makes nearby rays move toward one another. It is diverging if it makes them spread apart.
A convex lens is usually a converging lens. Parallel rays can be brought to a focus, which is why a magnifying glass can concentrate sunlight.
A concave lens is usually a diverging lens. It spreads rays outward.
A concave mirror can converge rays and form real images in front of the mirror.
A convex mirror tends to diverge rays and forms smaller virtual images.
Everyday examples
Cameras use converging lenses to form real images on a sensor.
Magnifying glasses use a convex lens to make nearby objects appear larger.
Makeup or shaving mirrors are often concave, because at close distances they can produce a larger upright virtual image.
Car side mirrors are often convex, because they give a wider field of view, though objects appear smaller.
The deep idea is simple: an optical element does not “copy” an object. It redirects rays in a predictable way, and the image is the geometric result of that redirection.
A simple ray diagram for a convex lens
A convex lens is thicker in the middle than at the edges. For a beginner ray diagram, three words matter most.
The principal axis is the main horizontal reference line through the center of the lens.
A focal point is a point on the axis where rays that were parallel to the axis are brought together by the lens, at least in the thin-lens approximation.
The image location is the point where the refracted rays meet, or appear to meet.
You usually do not need many rays. Two are enough to understand the picture.
The two principal rays
Parallel ray. Draw a ray from the top of the object parallel to the principal axis. After passing through the convex lens, it goes through the focal point on the far side.
Central ray. Draw a ray from the top of the object through the center of the lens. In the thin-lens model, it continues straight without noticeable bending.
Where those two rays cross, that is where the top of the image is. If the rays meet on the far side of the lens, the image is real. For the usual case of an object beyond the focal point, the image is also inverted.
The beginner mistake is to memorize the lines without knowing why they matter. The point of the diagram is not the artwork. The point is that each line stands for a possible path of light, and the crossing point tells you where light from one point on the object is brought together.
When geometrical optics works well
Geometrical optics works well when the straight-ray picture is a good approximation. That includes many everyday situations involving mirrors, lenses, eyeglasses, cameras, and large-scale image formation.
It becomes incomplete when the wave nature of light can no longer be ignored. Two important wave effects are:
Diffraction: light spreading around edges or through small openings
Interference: overlapping light waves reinforcing or canceling one another
Those effects are not handled well by a pure ray picture. If you want to explain sharp lens images, a mirror reflection, or why a straw looks bent in water, geometrical optics is often enough. If you want to explain colors in thin films, diffraction patterns, or why light spreads after a narrow slit, you need wave optics.
A practical rule is this: use geometrical optics when the setup is large compared with the wavelength of light and the main question is where rays go and where images appear. That is why the model remains so useful. It is simple, visual, and often exactly the right level of description.