# PHYS 2212 Module 13

13: The Nature of Light

Due to total internal reflection, an underwater swimmer’s image is reflected back into the water where the camera is located. The circular ripple in the image center is actually on the water surface. Due to the viewing angle, total internal reflection is not occurring at the top edge of this image, and we can see a view of activities on the pool deck. (credit: modification of work by “jayhem”/Flickr)

Our investigation of light revolves around two questions of fundamental importance: (1) What is the nature of light, and (2) how does light behave under various circumstances? Answers to these questions can be found in Maxwell’s equations (in Electromagnetic Waves), which predict the existence of electromagnetic waves and their behavior. Examples of light include radio and infrared waves, visible light, ultraviolet radiation, and X-rays. Interestingly, not all light phenomena can be explained by Maxwell’s theory. Experiments performed early in the twentieth century showed that light has corpuscular, or particle-like, properties. The idea that light can display both wave and particle characteristics is called wave-particle duality, which is examined in Photons and Matter Waves.

In this module, we study the basic properties of light. In the next few modules, we investigate the behavior of light when it interacts with optical devices such as mirrors, lenses, and apertures.

We just learned that light is a wave (an “electromagnetic wave”, with very small wavelength). But in many cases, you can safely ignore the wave nature of light. Light was studied for a long time (obviously), long before Maxwell, and it was very well understood. People thought about light as sort of like a stream of “particles” that travel in straight lines (called “light rays”). Unlike particles, waves behave in funny ways – e.g. they bend around corners. (Think of sound coming through a doorway.) But, the smaller the λ is, the weaker these funny effects are, so for light (with very small λ), no one noticed the “wave nature” at all, for a long time. The wavelength of light is 100’s of times smaller than the diameter of a human hair.

For this module and the next, we’ll study the more “classical” aspects of light, called GEOMETRICAL OPTICS – the study of how light travels, and how we perceive and manipulate it with mirrors and lenses.

We will ignore time oscillations/variations (1014 Hz is too fast to notice, generally!) We’ll assume light travels in straight lines (at 3 × 108 m/s, super fast). Light can then change directions in 3 main ways:

1. Bouncing off objects = reflection
2. Entering objects (e.g. glass) and bending = refraction
3. Bending around objects = diffraction. This is the place where the wave nature of light really comes into play.

How do you know where objects are? How do you see them?

You deduce the location (distance and direction) in complicated physiological and psychological ways, but it arises from the angle and intensity of the little “bundle” of light rays that make it into your eye.

If light bounces off a smooth surface (like a mirror, or a lake), it’s called “specular reflection”, and it is always true that

θi = θr , “angle of incidence” = “angle of reflection”.

If light bounces off a dull surface (like e.g. white paper, or a wall), it’s called “diffuse reflection”, and the light comes out every which way. (Microscopically, “dull” means that the surface is not smooth on the scale of the wavelength of light.)

By the way, the “angle of incidence = angle of reflection” rule from a smooth surface (e.g. a shiny metallic surface) arises from Maxwell’s equations! ALL of the classical properties of light ultimately arise from these fundamental underlying equations!)

Any transparent medium (air, H20, glass, …) that lets light through will have a number n, the “index of refraction”, associated with it. n is determined by how fast light travels through the material. (Light only travels at c, the “speed of light”, in vacuum. In materials, it is slowed down.) The bigger n, the slower the light travels:

n = c/v = speed of light in vacuum / speed of light in medium

n = c / v = (3 x 108 m/s) / v

If light goes from one medium into another, it will (in general) bend, i.e. change it direction. This is called refraction. There is a formula for the refraction of light derivable from Maxwell’s Equations, called Snell’s Law:

n1sinθ1 = n2sinθ2

#### 13.1 The Propagation of Light

• Determine the index of refraction, given the speed of light in a medium
• List the ways in which light travels from a source to another location

#### 13.2 The Law of Reflection

• Explain the reflection of light from polished and rough surfaces
• Describe the principle and applications of corner reflectors

#### 13.3 Refraction

• Describe how rays change direction upon entering a medium
• Apply the law of refraction in problem solving

#### 13.4 Total Internal Reflection

• Explain the phenomenon of total internal reflection
• Describe the workings and uses of optical fibers
• Analyze the reason for the sparkle of diamonds

#### 13.5 Dispersion

• Explain the cause of dispersion in a prism
• Describe the effects of dispersion in producing rainbows

#### 13.6 Huygens’s Principle

• Describe Huygens’s principle
• Use Huygens’s principle to explain the law of reflection
• Use Huygens’s principle to explain the law of refraction
• Use Huygens’s principle to explain diffraction

#### 13.7 Polarization

• Explain the change in intensity as polarized light passes through a polarizing filter
• Calculate the effect of polarization by reflection and Brewster’s angle
• Describe the effect of polarization by scattering
• Explain the use of polarizing materials in devices such as LCDs