April 4 Physics 54 LectureProfessor Henry Greenside

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Today’s Topics

Chapter 33: “Refection and Refraction”• The ray model of light• Reflection from planar mirrors.• Reflection from curved mirrors.

The Ray Picture:Small Wavelengths, Far From Source

Geometric Optics: The Ray Picture of Light

When light has a wavelength much smaller than objects that it interacts with, we can treat light as composed of straight-line rays.

This regime is called geometric optics.

When this assumption fails, have to worry about wave properties, namely interference and diffraction which we discuss later this semester.

Properties of Light Rays

1. Light rays travel in straight lines.

2. Light rays can cross (superposition, no interaction).

3. Light ray travels forever unless it interacts with matter (reflection, refraction, absorption).

4. Each point of an object emits light rays in all directions.

5. Eye sees by focusing light rays from different points.

Example of Ray Model: Shadow of Letter L

Wavelength of light must be much smaller than width of slots or holes in screen!

PRS: What Pattern of Light on Screen?

Law of Reflection

reflection of angle incidence of angle :2 Rule ri

Rule 1: Incident ray, normal, and reflected ray all lie in same plane.

Note: all angles are measured with respect to the normal at point of interest!

Vocabulary and Geometry

1. do = object distance from mirror2. di = image distance from mirror3. Image is virtual as opposed to real since no actual light

passes through actual location of the perceived image.4. Image is upright as opposed to inverted, i.e., image has

same orientation as object.

Key Geometric Trick for Planar Mirrors

Thou shalt draw a perpendicular bisector from theobject through the mirror, and maybe more than one if necessary.

Look for similar triangles to relate various quantities.

Question: How Many Orange Ball Images and In Which Directions Can Be Seen from Pink Dot?

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One Can Also Locate The Same Images By Reflecting the Eye Position Rather Than the Orange

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Law of Reflection Holds for Billiards!

Whiteboard Examples of Reflection off Planar Mirror

1. How to choose smallest size of dressing mirror to see entire body in mirror. Note that answer does not depend on distance of person to mirror!

2. How to deduce the size of the rearview mirror of a car (make sure to review how to use similar triangles). Assume rear view window is rectangle of dimensions 0.3 m by 1.3 m, that rearview mirror sits 0.5 m from eyes, and that rearview mirror is 1.5 m from rearview window. Then what should minimum dimensions of mirror be to see entire rear window without turning head? Answer: 16 cm by 3.8 cm.

The Principle of Least TimeBrief white board discussion: geometric construction suggests that light travels shortest distance (distance between two points) which is same as shortest time.

This turns out to be a deep principle of Nature: many phenomena including mechanical motion of particles, waves satisfying Maxwell equations, the Schrodinger equation, have dynamics that minimize some quantity called the Lagrangian of the dynamics.

Minimization principles do not hold for open non-equilibrium systems such as biological organisms, ecologies, the atmosphere, snow flakes. These are much harder phenomena to understand in principle.

New Yorker Cartoon Errors?

How many errors are there in this New Yorker Cartoon?1? 2? 3? 4?

Lunar Corner Reflectors

A mathematical challenge: prove that the outward ray is always parallel to incoming ray for corner reflector.

A conceptual challenge: if you look into such a corner reflector, is your face reversed or not?

Law of Reflection Holds Locally on Curved Mirrored Surfaces

Mnemonic: Looking at a concave mirror is like looking into a “cave”, the light has to enter a surrounding region. A convex mirror is then the “other” kind of mirror.

Concave Spherical Mirrors Can Focus Light

Spherical aberration: parallel rays do not all focus

Concave-mirror Eyes of Scallops and Clams

Paraxial Rays Approximately Focus to a Point F

2

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C = center of spherical or circular arcF = focus of spherical mirrorf = distance from center A of mirrorr = radius of spherical mirrorparaxial rays: all angles small enough