Turn in your homework in the boxes at the back of the lecture hall on your right as you face the back of the hall.

Lectures from chapter 1 are on the website Clickers will be counted starting today, remember we drop the five lowest lecture session scores. Phosphorescence demo

Chapter 2: Geometrical Optics Geometrical Optics –Ray tracing –For objects much larger than the wavelength of light Shadows –Extended sources –Eclipses –Pinhole cameras Reflection –Wave picture –Radar and sonar Mirrors

Geometrical Optics Allows us to avoid thinking about all the details of wave propagation of light Also called “ray optics”, because it is sufficient to use only light rays to describe the propagation Is only valid when the objects being considered are much larger than the wavelength of the light

Point Light Sources An idealized light source, can be approximated by a small light bulb or a candle, or even a star, if you are far enough away from it. Remember that rays only tell us the direction of the light, not its intensity. We need wave theory to explain why light gets dimmer further away.

Shadows Appear when light rays from a source are blocked by an object Rays that ARE blocked by the book Point light source Book Shadow Rays that are NOT blocked by the book What happens when we move the screen back?

Clicker Question What happens to the shadow when we move the screen back? a) gets biggerb) stays the samec) gets smaller Rays that ARE blocked by the book Point light source Book Shadow Rays that are NOT blocked by the book

Shadows from two sources 2 point light sources Book Wall A B Blocked by book umbra The two parts of the penumbra each get light from only one of the two bulbs. The umbra gets no light from either of the two bulbs. The bright region gets light from both of the bulbs. penumbra umbra

Shadows from an extended source penumbra umbra

The Sun, the Moon, and Shadows

Solar Eclipse Geometry The umbra is usually only a few hundred kilometers across and the total eclipse lasts only a few minutes

Eclipse Path

Solar Eclipse

Lunar Eclipse Geometry

Lunar Eclipse A lunar eclipse can be viewed over a much larger area and for a much longer period of time than a solar eclipse

Red Moon At the point of total eclipse, the moon appears red This is due to the scattering of sunlight by the earth’s atmosphere, similar to a sunset

Looking back at Shadows Theoretically we can reconstruct the object and light source from the shadow In general, it is blurry and complicated

Pinhole Cameras Light rays from each point on the object reach one point on the screen, and no rays from other points on the object reach that same point on the screen. Pinhole camera Image Object

Pinhole Cameras Note that the object does not have to be self- luminous. The rays reflected from a light source will also enter the pinhole and can image the object. Pinhole camera Image Object

Clicker Question Which camera will produce the smallest image of the light bulb? A B C D, they are the same size A B C

Clicker Question Which camera will produce the smallest image of the light bulb? A B C D, they are the same size A B C

Camera Obscura Essentially a room sized pinhole camera

Camera Obscura, San Francisco < Pictures from LIFE magazine in 1954 Images from 2008 v

Camera Obscura Images A projection of an image of the New Royal Palace in Prague Castle created with a camera obscura

Camera Obscura Images Photographer Abelardo Morell Camera Obscura: View of Central Park Looking North-Fall, 2008

Reflection (return to waves) Light waves travel in a straight line until they hit a different medium Reflections of any kind of wave occur whenever the medium of propagation changes abruptly, e.g. rope tied to a wall or a string What counts is the change in the wave’s speed of propagation. If no speed change occurs, there is no reflection If the speed changes dramatically, most of the wave is reflected. If there is little change in speed, little reflection occurs

Speed of Light Waves

Transmission and Reflection Incident ray Transmitted ray Reflected ray The incident ray causes electrons in the material to oscillate, which generates a new wave. Some of this new wave travels backwards as the reflected wave, some travels forward, and combines with the incident wave as the transmitted wave.

Radar and Sonar Both radar (radio waves) and sonar (sound waves) use wave reflections to determine the position and speed of distant objects Note: Sonar does not use electromagnetic waves, but sound waves

Glass and Metal So why is glass transparent and metal reflective? For the same reason that metal conducts electricity and glass does not: Metals have a lots of electrons that are not attached to anything, and can thus move (conduct electricity) or oscillate when illuminated by a light wave.

Metals and Mirrors The many oscillating electrons in metals can generate a forward traveling wave that exactly cancels the incident wave, so all the light is reflected. Metals thus appear opaque, and make excellent reflectors (mirrors)

Metals and Mirrors Metals are only good reflectors for certain wavelengths. At high frequencies, the electrons can’t move fast enough to keep up with the light wave and cancel the forward going wave, thus some of the wave is transmitted and the wave is not reflected well. Different metals have different cutoff wavelengths, called the plasma frequency, which gives them different colors. silvergoldcopper

Ionosphere Extends miles from the earth’s surface Composed of electrically charged gas particles Plasma frequency: 10 8 Hz AM radio frequencies: 10 6 Hz

Silver Mirrors Silver tarnishes (turns black) very easily, and front surface mirrors are easily damaged. Most common silver mirrors are plated on the back surface, to avoid this. The problem with back surface mirrors is that there are often multiple reflections from the glass surfaces.