Geometric optics is all about tracing rays of light.
This lets us understand mirrors, lenses, shadows, eyeglasses, microscopes, telescopes, solar eclipses, etc.
Motivating images: How do rainbows form? UK Instagrammer Anthony Killeen (t_killeen37) took this photo at New Zealand’s Bay of Islands
How is the water changing the way that light moves?
The ray model of light
Treat light as if it is made of particles that travel in straight lines.
We’ll call these particles photons.
no electric charge
they carry energy and momentum
They can interact with other particles, such as electrons.
When in empty space, they travel at the speed of light
Here we see rays of light moving from a sign, into an eye, and focusing on the retina.
We light travelling in rays, in nature
Caution: Saying light moves in straight lines is only an approximation. Light actually travels as waves.
Really? In some ways, light travels like water waves? Yup. But for now, we start with light travelling in straight lines – and then add on the wave nature of light next week.
When light hits a reflective surface, its incident angle is the same as its reflected angle.
Many objects depend on reflections, such as mirrors.
Greek letter theta, θ, represents “angle”
θi = angle of incidence
θr = angle of reflection
Here’s light reflecting off of a mirror on the wall.
Here, water waves, or light waves, hit a curved surface
The wavefronts reflect to a point, called the focus.
Now we can see how a mirror works
Look at the rays of light from the mirror, especially the ones that end up in the person’s eyes.
Why learn these techniques?
We’re going to learn certain facts and skills. With some practice we’ll become good at problem solving. Why learn such problem solving skills at all?
Lenses and Images
On Optical instruments (Kaiser science) we cover
Convex lens (converging lens), Concave lens (diverging lens)
Virtual vs. Real Images
Cameras; the human eye; nearsightedness and farsightedness
Magnifying glass; telescopes
Aberrations of Lenses and Mirrors
Refraction of light
from The Law of Refraction, OpenStax College
How can we see the same fish, as if it is in 2 different places?
“because light changes directions when it passes from water to air. In this case, the light can reach the observer by two different paths, and so the fish seems to be in two different places. This bending of light is called refraction and is responsible for many optical phenomena.”
Why does light change direction when passing from one material (medium) to another
Light changes speed when going from one material to another.
Here is an analogy.
The change in direction of a light ray depends on how the speed of light changes when it crosses from one medium to another.
The speed of light is greater in medium 1 than in medium 2 in the situations shown here
(a) A ray of light moves closer to the perpendicular when it slows down.
This is analogous to what happens when a lawn mower goes from a footpath to grass.
(b) A ray of light moves away from the perpendicular when it speeds up.
This is analogous to what happens when a lawn mower goes from grass to footpath.
The paths are exactly reversible.
– from The Law of Refraction, OpenStax College
Staying on the same topic, let’s trace parallel rays of light, as they move from the air (low index of refraction) into water (low index of refraction)
Speed of light slows down in the water.
Here we see the same thing, but now the rays of light are more realistic.
They emanate from a source, so they aren’t really parallel.
Yet when the rays hit the water, they are approximately parallel, so the result is the same.
New section here
A prism separates white light into many colors
How? Each wavelength of light refracts by a different amount
The result is dispersion – each wavelength is bent by a different amount
A mirage is a naturally occurring optical phenomenon in which light rays are bent to produce a displaced image of distant objects or the sky. Our lesson on mirages.
Take a laser pointer and direct it down into the paper, in the direction of the reflector. Then gently raise the tip of the laser and a bright spot mimicking a pulse of light moves along the paper in the direction of the mirror. Continue raising and lowering the pointer to create a moving ‘light pulse’ in both directions. Simple but very effective!
Giancoli Physics, Chapter 23
23.1: The Ray Model of Light
23.2: Reflection; Image Formation by a Plane Mirror
23.3: Formation of Images by Spherical Mirrors
23.4: Index of Refraction
23.5: Refraction: Snell’s Law
23.6: Total Internal Reflection; Fiber Optics
23.7: Thin Lenses; Ray Tracing
23.8: The Thin Lens Equation
23.9: Combinations of Lenses
23.10: Lensmaker’s Equation
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling within various media. Recognize that electromagnetic waves can travel through empty space (without a medium) as compared to mechanical waves that require a medium
HS-PS4-3. Evaluate the claims, evidence, and reasoning behind the idea that electromagnetic radiation can be described by either a wave model or a particle model, and that for some situations involving resonance, interference, diffraction, refraction, or the photoelectric effect, one model is more useful than the other.
HS-PS4-5. Communicate technical information about how some technological devices use the principles of wave behavior and wave interactions with matter to transmit and capture information and energy. Emphasis is on qualitative information and descriptions. Examples of principles of wave behavior include resonance, photoelectric effect, and constructive and destructive interference.
SAT subject test in Physics: Waves and optics
• General wave properties, such as wave speed, frequency, wavelength, superposition, standing wave diffraction, and Doppler effect
• Reflection and refraction, such as Snell’s law and changes in wavelength and speed
• Ray optics, such as image formation using pinholes, mirrors, and lenses
• Physical optics, such as single-slit diffraction, double-slit interference, polarization, and color
A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)
PS4.A: WAVE PROPERTIES
When a wave passes an object that is small compared with its wavelength, the wave is not much affected; for this reason, some things are too small to see with visible light, which is a wave phenomenon with a limited range of wavelengths corresponding to each color. When a wave meets the surface between two different materials or conditions (e.g., air to water), part of the wave is reflected at that surface and another part continues on, but at a different speed. The change of speed of the wave when passing from one medium to another can cause the wave to change direction or refract. These wave properties are used in many applications (e.g., lenses, seismic probing of Earth)… the wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing. The reflection, refraction, and transmission of waves at an interface between two media can be modeled on the basis of these properties… At the surface between two media, like any wave, light can be reflected, refracted (its path bent), or absorbed. What occurs depends on properties of the surface and the wavelength of the light…. Lenses can be used to make eyeglasses, telescopes, or microscopes in order to extend what can be seen. The design of such instruments is based on understanding how the path of light bends at the surface of a lens.