• Unit 7: Optics

    An optical phenomenon involves an interaction between electromagnetic waves and matter. The complete study of optics involves complex mathematics, a thorough understanding of both classical and quantum optical effects, and a great deal of engineering.

    We begin by applying simplified models to develop a basic understanding of how optics works, without having to remember all of Maxwell's equations. In geometric optics, we ignore all the effects that are germane to waves, such as interference. This will nevertheless allow us to understand a large variety of phenomena. We will return to the complexities of wave physics as related to optics in the section on wave optics at the end of this unit.

    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

      • The Ray Model of Light URL

        Read chapter 28 on pages 814–826. It introduces the phenomena of reflection and refraction. Answer the self-check question (answer on page 1012). Think about the discussion questions and examples, and solve the problems on pages 829–830.

      • Reflection and Refraction Page

        Watch this lecture series.

      • Geometric Optics URL

        Read these sections. Work through examples 12.1 and 12.2 before looking at the solutions.

      • Specular and Diffuse Reflection URL

        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.

      • Snell's Law of Refraction URL

        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.

      • Total Internal Reflection URL

        When a light ray is within a medium having a refractive index n1 and is incident on an interface between that medium and a second medium having a smaller refractive index n2, Snell's Law tells you that the angle at which the light is refracted in the second medium is given by sin θ2 = (n1/n2) sin θ1.

        What happens if (n1/n2) sin θ1 is greater than 1? Because sin θ2 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 metalized 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.

      • Rainbows URL

        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

      • Mirrors and Lenses Page

        Watch this lecture series.

      • Paraxial Optics URL

        Read these sections. Work through examples 13.1–13.4 before looking at the solutions.

      • Ray Diagrams for Lenses URL

        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

      • Wave Optics URL

        Read the sections "Introduction", "Huygens' Principle", and "Young's Double-Split Experiment". Work through example 14.1 before looking at the solution.

      • Interference of Light Waves Page

        Watch this lecture series.

      • Two-Slit Constructive and Destructive Interference URL

        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

      • Unit 7 Assessment Quiz

        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.