Lecture 21: Introduction to Light Waves

Light is an electromagnetic transverse wave composed of oscillating electric and magnetic fields.
It does not require a medium to travel through, disproving the Ether hypothesis.
The speed of light in a vacuum is $3 × 10^8 m/s$ , which is the speed limit of the Universe.
Interactions with atoms and molecules in fluids and solids can reduce the average speed due to absorption and re-emission.
The speed of light appears to be the same to any observer, regardless of their motion.

“Optical” or “Visible” Light is the narrow band of light frequencies detectable by the human eye.
The light spectrum is broad, with our eyes detecting only a tiny fraction.

Light comes from many sources and has many uses and benefits for life, but it can also cause harm.
The atmosphere protects us from much of the harmful light.

Light is fast, but space is vast.
It takes 8 minutes for light from the Sun to reach the Earth.
If the Sun stopped producing light, we wouldn’t know until 8 minutes later.
Similarly, if the Sun disappeared, we wouldn’t feel the effects until 8 minutes later, as gravity waves travel at light speed.
It takes nearly an hour for sunlight to reach Jupiter and 1.5 hours for Saturn.
The Voyager probes, launched in 1977, are about three times the distance of Pluto from the Sun.
The nearest star system, Proxima Centauri, is about 4 light-years away.
The Milky Way Galaxy is about 90,000 light-years wide.
The distance to the Canis Major Dwarf Galaxy is about 25,000 light-years from the galactic center.
The Small and Large Magellanic Clouds are 180,000 - 200,000 light-years away.
Andromeda is 2,537,000 light-years away.
The Sculptor Group is about 12,000,000 light-years from the Milky Way’s center.

Wave Model: Describes how light waves spread out and how the superposition of multiple light waves causes interference. The study of light as a wave is called wave optics.
Ray Model: Light travels in straight lines, which explains how mirrors and lenses work. The properties of prisms, mirrors, and lenses are best understood in terms of light rays. The ray model is the basis of ray optics.
Photon Model: In the quantum world, light consists of photons that have both wave-like and particle-like properties. This is the quantum theory of light.

At large enough distance scales compared to the wavelength of light $(d ≫ λ)$ , light motion can be treated as a “ray,” traveling in a straight line until absorbed or reflected.
For optical light and everyday life, this approximation works well.
If distance scales are near or below the wavelength $(d ~ λ)$ , Geometric Optics is insufficient to describe observations like interference and diffraction.
Approximating light as a “ray” simplifies motion to geometry and trigonometry.

Diffraction is the ability of a wave to spread out after passing through a small hole or going around a corner.
The diffraction of light indicates that light is a wave.
A smaller hole causes more spreading.

A water wave spreads out after passing through an opening, filling the space behind it.
This spreading of waves is called diffraction.

Unlike a water wave, light passing through a large opening makes a sharp-edged shadow.
This lack of noticeable diffraction means that if light is a wave, the wavelength must be very small.
When red light passes through an opening only 0.1 mm wide, it does spread out.
Diffraction of light is observable if the hole is sufficiently small.

Constructive Interference:
- $y_1(x, t) = A \sin(kx - wt)$
- $y_2(x, t) = A \sin(kx - wt)$
- $y(x, t) = y<em>1 + y</em>2 = 2A \sin(kx - wt)$
Destructive Interference:
- $y_1(x, t) = A \sin(kx - wt)$
- $y_2(x, t) = A \sin(kx - wt + π)$
- $y(x, t) = y<em>1 + y</em>2 = 0$

The wave from the lower slit travels an extra distance: $\Delta r = d \sin \theta$
Bright fringes (constructive interference) occur at angles $\theta_m$ such that $\Delta r = d \sin \theta = mλ$ , where $m = 0, ±1, ±2, ±3, …$
Interference minima (destructive interference) occur when $\Delta r = d \sin \theta = (m + \frac{1}{2})λ$ , where $m = 0, ±1, ±2, ±3, …$
The mth bright fringe emerging from the double slit is at an angle: $\theta_m = m \frac{λ}{d}$ , where $m = 0, ±1, ±2, ±3, …$
$\theta_m$ is in radians, and the small-angle approximation is used.
The y-position on the screen of the mth bright fringe on a screen a distance L away is: $y_m = m \frac{λL}{d}$ , where $m = 0, ±1, ±2, ±3, …$

If the screen is moved farther away from the slits, the fringes will be farther apart.

A double-slit interference pattern is observed on a screen 1.0 m behind two slits spaced 0.30 mm apart.
Ten bright fringes span a distance of 1.7 cm.
We want to find the wavelength of the light.
The fringe spacing $\Delta y$ is uniform.
Ten bright fringes have nine spaces between them.
The fringe spacing is: $\Delta y = \frac{1.7 cm}{9} = 1.89 × 10^{-3} m$
Using this fringe spacing, we find that the wavelength is: $λ = \frac{d}{L} \Delta y = 5.7 × 10^{-7} m = 570 nm$
It is customary to express the wavelengths of visible light in nanometers.