### Unit 7: Optics

An optical phenomenon involves the interaction between electromagnetic waves and matter. We will focus on visible, infrared, and ultraviolet light, but much of the study of optics will apply to some extent to radio waves and x-rays. The complete study of optics involves enormously complex mathematics, a thorough understanding of both classical and quantum optical effects, and a great deal of ingenuity for success.

For the purposes of this course, optics will be limited to the classical description of electromagnetism provided by Maxwell's equations: the full wave optics. Even this level of description is quite complicated for most optical phenomena, so we will apply simplified models to develop a basic understanding of how optics works. In geometric optics, we assume that all light travels in straight lines. In paraxial optics, we assume that all optical systems handle light rays near a symmetry axis of the optical system, which allows us to largely ignore aberration, a vast array of terribly complex optical effects.

**Completing this unit should take you approximately 11 hours.**

Upon successful completion of this unit, you will be able to:

- determine the size, location, and nature of images by using the mirror and lens equations;
- solve problems using the law of refraction;
- describe the interference pattern in a double-slit experiment and explain experiment's results; and
- explain how rainbows are produced.

### 7.1: Geometric Optics

Read sections one through four of “Chapter 28: The Ray Model Of Light” (pages 814-826), which will serve as an introduction to the following the Khan Academy lecture series on the phenomena of reflection and refraction. Answer the Self-Check question in the text (answer on page 1012). Think about the Discussion Questions and Examples, and work out the six problems on the page 829-830.

Watch this lecture series, pausing to take notes, before moving on to the reading below.

Read these sections. Select the links for Examples 12.1 and 12.2, and work through these examples before looking at the solutions. Make sure you understand not only the solutions but how to approach solving the problems so that you can obtain the solutions yourself. Make sure you understand not only the solutions but how to approach solving the problems so that you can obtain the solutions yourself. You will be responsible for being able to solve problems of this type on the Final Exam.

This demonstration illustrates the difference between specular reflection (like a mirror) and diffuse reflection (like a piece of paper). There is a continuum of behaviors between specular and diffuse reflection, and these are well-illustrated in this demonstration. Note that the key is not the amount of incident light reflected, but rather the extent to which information about the original direction of the light is lost in the reflection. The demonstration may run slowly on older computers.

This demonstration illustrates the way in which light bends at an interface between the two media. Use this worksheet as a guide when exploring this demonstration.

When a light ray is within a medium having a refractive index n

_{1}and is incident on an interface between that medium and a second medium having a smaller refractive index n_{2}, Snell's Law tells you that the angle at which the light is refracted in the second medium is given by sin θ_{2}= (n_{1}/n_{2}) sin θ_{1}.What happens if (n

_{1}/n_{2}) sin θ_{1}is greater than 1? Because sin θ_{2}cannot be greater than 1, the light ray cannot be refracted into the second medium. As a result, the ray is reflected from the interface. The reflection is total (neglecting possible processes of absorption which might occur right at the interface, such as in dye molecules or the like), because there is no mechanism whereby any of the light can penetrate into the second medium. (This is actually only the case for infinitely thick media, as light can penetrate a distance related to the skin depth. However, for most practical purposes the reflection is complete.)Total internal reflection is unlike reflection from a metallized mirror, in which the metal absorbs some of the light incident on the surface. This difference explains why the reflecting face of a prism is usually left unmetallized whenever that is consistent with its optical function; more light passes through the optical system than does when a mirror is used.

The color of a rainbow results from variable dispersion of different wavelengths of light, but this demonstration goes further in illustrating why the rainbow appears in a circular bow in the sky.

### 7.2: Paraxial Optics

Watch this lecture series, pausing to take notes, before moving on to the reading below.

Read each section. Select the links for Examples 13.1 through 13.4, and work through examples before looking at the solutions. Make sure you understand not only the solutions but how to approach solving the problems so that you can obtain the solutions yourself. Make sure you understand not only the solutions but how to approach solving the problems so that you can obtain the solutions yourself. You will be responsible for being able to solve problems of this type on the Final Exam.

This demonstration illustrates the dynamics between focal length, object distance, and real/virtual focal points of a simple lens. Explore this demonstration for both convergent and divergent lenses. Drag the object closer to the lens and observe how the magnification changes with distance. Pay attention to the path of the rays. Notice that for the convergent lens, at some point the image changes from real to virtual. How far is the object from the lens at this point? Change the height of the object and repeat the procedure. Does the same thing happen again?

### 7.3: Wave Optics

Read the "Introduction," "Huygens’ Principle," and "Young’s Double-Split Experiment" sections. Select the links to Example 14.1 , and work through the example before looking at the solution. Make sure you understand not only the solution but how to approach solving the problem so that you can obtain the solution yourself. You will be responsible for being able to solve problems of this type on the final exam.

Watch this lecture series, pausing to take notes.

Interference is a nearly ubiquitous effect in wave optics. This demonstration illustrates how light waves interfere both constructively and destructively. The electric vector of the electromagnetic radiation is shown waves moving from the slits. When you examine the diffraction image, the points of constructive interference (where the two electric fields add) appear red, while the points of destructive interference (where the two electric fields cancel) appear white.

### Unit 7 Assessment

Take this assessment to see how well you understood this unit.

- This assessment
**does not count towards your grade**. It is just for practice! - You will see the correct answers when you submit your answers. Use this to help you study for the final exam!
- You can take this assessment as many times as you want, whenever you want.

- This assessment