Ch23 Ray Optics 講者： 許永昌 老師

Contents 當您在學這一章時，請常常想何時可以使用Ray Model，這樣做，您就會對何時該用Ray Model何時該用Wave Model 有比較清楚的認識。 The Ray Model of Light Object Eye Ray diagram and Ray tracing Aperture Reflection Specular reflection Diffuse reflection The Plane Mirror Refraction Snell’s Law (derived from Wave model) Image formation by Refraction. Color and dispersion (實驗11) Thin Lenses: From Ray tracing From Refraction Theory

The Ray Model of Light (請預讀P700~P701) A light ray is An abstract idea. A line in the direction along which light energy is flowing. The Ray Model of Light: Light rays travel in straight lines. Light rays can cross. A light ray travels forever unless it interacts with matter. An object is a source of light rays. Every points and all directions. The eye sees by focusing a diverging bundle of rays.

Action Purpose: Get the feeling of Ray Model Objects: Action: 1 laser pen. A light bulb. Action: How to represent a laser beam by Ray Model? Parallel bundle Can you predict the size of a shadow? Point source

Ray diagram and Ray tracing (請預讀P702 & P716) We use a few special rays to describe the behavior of infinitely many rays. For example, we use three principle rays for each point of an object to find the image. Example: A pinhole Camera Stop to think: The relation between h0, d0, d1 and h1.

Exercise Hint: The light rays fill the aperture.

Reflection (請預讀P703~P705) Reflection: Specular reflection: Reflection from a flat, smooth surface. Properties: The incident ray and the reflected ray are in the same plane normal to the surface. qi=qr. NOTE: Optics calculations always use the angle measured from the normal. Examples: Mirror, polished metal,… Defuse reflection: Reflection from a rough surface. Examples: (objects) Friends, walls, pages, … 所以，大部份日常看到的都是這類。 這兩個properties其實由Wave Model可以得到解釋。

Exercise Plot the light rays emitted from a point source reflecting from a plane mirror. How do you see this point source? Hint: diverging rays. Where is the virtual image?

Homework Student Workbook 3, 6, 7, 9, 10

Refraction (請預讀P706~P711) Phenomena: When a light ray is incident on a smooth boundary between two transparent materials, Part of the light reflects from the boundary, The law of reflection. Part of the light continues into the second medium with a change in direction, is called refraction. Snell’s law of refraction. n1sinq1= n2sinq2. Where n=c/vmedium. Hint: f and l//. incident interface Reflected Refracted Angle of refraction

Total internal reflection (TIR) and Fiber Optics From Snell’s Law we get If n1/n2sinq1 >1, the refraction is forbidden and 100% of the light reflects from the boundary. This process is called TIR. Condition: n1>n2. q1>qc=sin-1(n2/n1). qc is called critical angle. Examples: Glass  air: qc=sin-1(1.00/1.50)=42o.

Action Purpose: Objects: Action: Get the feeling about the reflection and refraction. Objects: One tank of water Soda dust Laser pens Fiber Action: Send a laser (or lasers) beam into the water with soda Observe the behavior of reflection and refraction. Send a laser beam into the fiber.

Image Formation by refraction(請預讀P712) Model: The object and observer are on the optical axis (perpendicular to the boundary). Paraxial rays: (Rays are nearly parallel to the axis.) q~tanq~sinq. We get

Homework Student Workbook 12, 14, 16, 17

Color and Dispersion (請預讀P713~P716) It is associated with the frequency of light; however, we see the color is related to how our visual system responds to EM waves. Example: Colored objects: absorb what? Dispersion: Reason: Index of refraction is the function of frequency, i.e. n(f). f   n usually. Examples: Rainbows Rayleigh scattering: (Assume that each molecule is as a dipole whose pE) Iscattering f 4. Examples: Blue Skies and Red Sunset (請回家觀察).

Homework Student Workbook 18, 20

Thin Lenses: Ray Tracing (請預讀P717~P721) Qualitative Converging and Diverging Lenses Important sets of rays for analysis: We use them to plot the Ray-tracing diagram. Converging Lens Diverging Lens

Action Purpose: Objects: Action: Get the feeling of focal point and principle rays. Objects: One tank of water +Soda Laser pens Lens Action: Send the parallel laser beams Observe the focal point. Send laser beams from one point. (Maybe I need the cardboard)

Exercise Draw the Ray-tracing diagrams of Real or virtual image? Focal point Focal point

Lateral Magnification Because any ray directed at the center of the lens passes through in a straight line, we can find that |h’|/|h|=|s’|/|s|. People define and Positive Negative h and h’ s (object) Real image (object) Virtual image s’ (image) Real image s’ s h h’

Homework Student workbook 23, 24, 26, 27, 28

Thin Lenses: Refraction Theory (請預讀P722~P727) Quantitative Model: Small angles. Thin lens or almost flat boundary. Visualize: Solve: Finding the relationship between s and s’ of a spherical surface. (It also has two focal points whose lengths are not the same.) Finding the focal points of a thin lens. The focal lengths of a thin lens are the same. s s’ Positive Negative R Convex toward the real object Concave toward the object 本頁公式請自行參照課本。

Image Formation with spherical mirrors (請預讀P728~P731) Three important sets of rays: Stop to think: How to prove it?

Homework Student Workbook 29, 30, 31, 32, 33 這一章有許多容易混淆的定義，所以強烈建議一定要自行製作 Terms and Notation的卡片。