Properties of Light    Chapter 12  Joseph F. Alward, PhD  Department of Physics  University of the Pacific

Law of Reflection
 Angle of Reflection = Angle of Incidence  Angles are measured with  respect to the normal line  (the perpendicular line).

Reflection Law Example
 Example Problem:   90 - 65 = 25 180 - 120 - 25 = 35   90 - 35 = 55

Billiards and Mirrors
 A ball bouncing off the bank of a pool table behaves like a light ray reflecting off a mirror.  To bank the cue ball into another ball (the object ball), imagine you are shooting at the mirror image of the object ball. Billiards and Mirrors This applet allows placement and speed of cue ball.

Specular vs Diffuse Reflection

Diffuse Reflection
 Rough surfaces consist of a large number  of different specularly-reflecting planes. Visible light reflects diffusely from  paper.

Specular and Diffuse Reflection
 Rough surfaces seem smooth for very long-wavelength electromagnetic waves. This parabolic dish reflects long wavelength radio waves to the detector, but reflects most of the shorter wavelength radiation away from the detector.

Specular vs Diffuse Reflection
 The cruiser Aurora, which played an important role in the communist revolution in 1917, is docked on the River Neva at St. Petersburg, Russia. When the water is still, reflection is specular.  The image blurs when the water is rough. (Eugene Hecht, Physics)

Specular versus Diffuse Reflection
 What kind of reflections account for the column of light reflected off the water? What would we see on the water if it were perfectly flat, unmoving?

Plane Mirror Geometry
 Light from the castle appears to be  coming from a point behind the mirror

Virtual Images in Plane Mirrors
 If light energy doesn't flow from the image,   the image is "virtual". Rays seem to come from behind the mirror, but, of course, they don't.  It is virtually as if the rays were coming from behind the mirror. "Virtually":  the same as if As far as the eye-brain system is concerned, the effect is the same as would occur if the mirror were absent and the chess piece (castle) were actually located at the spot labeled "virtual image".

Image vs Object Distance
 Flat mirror images are as far behind the mirror as is the object.   About 4 percent of light is reflected off a windowpane.

The Law of Reflection
 The girl in Edouard Manet's painting,  The Bar at the Folies-Bergeres, is standing in front of a large plane mirror. We see reflected in it her back and the face of a man she seems to be talking to. From the law of reflection what if anything, is wrong with this painting? (Eugene Hecht, Physics)

The Law of Reflection
 The Toilet of Venus, by Diego Velasquez. What does Venus see in the mirror? (Eugene Hecht, Physics)

Left-Right Reversal
 The woman's image is as far behind the flat mirror as she is in front of it. Note the that "woman" in the mirror is coming her hair with her left hand.

Left-Right Reversal
 The printing is reversed when viewed in a rear- view automobile mirror.

Convex and Concave Mirrors
 Images in convex mirrors                                              Images in concave mirrors  are always smaller.                                                          are always bigger.

Convex Mirrors
 Images in convex mirrors are always smaller than the object. (M.C. Eshcher)

Convex Mirrors

The Hubble Mirror
 Images are always smaller in a convex mirror. What type of mirror is the Hubble mirror? What is the person in the mirror pointing at?

Concave Make-Up Mirror

Concave Mirror Focuses Colors
 White light is formed where red, blue, and green overlap.

Concave Mirror Focal Point
 Rays' paths are determined by the angle law.

Applets
 1.  Concave Mirror Animation     2.  Diverging Mirror

Refraction:  The Bending of Wavefronts
 One side of wave front slows down, and the entire train of fronts twists.

Understanding Refraction

Refraction Terminology
 Angles are measured with respect to the line which is perpendicular to the interface. When light travels from one medium--such as air, to another one of higher density--such as water, usually the light ray bends toward the perpendicular line.

Apparent Depth in Water
 Light exits into  medium (air)  of lower index  of refraction,  and turns left.

More Apparent Depth
 Spear-fishing is made more difficult by the bending of light. To spear the fish in the figure, one must aim at a spot in front of the apparent location of the fish.

 A FishEye's View of the World (Excellent applet illustrating refraction)

Refraction at Sunset
 The sun actually falls below below the horizon, i.e., it "sets", a few seconds before we see it set.

Flattening of the Sun at Sunset
 Bottom of sun appears flattened at sunset. Rays from top of sun are also  refracted, but not as much because  they enter the atmosphere at a less  oblique angle.  Thus, the top of the  sun is also flattened, but not as  much as the bottom.

 There's no water on the road; why does it appear so?

Explaining the Water Mirage

Differential Color Refraction
 Note that the shorter wavelengths of light are bent more than the longer; blue more than red.

Refraction in a Raindrop
 Violet is bent more than red.

Forming a Rainbow
 An observer sees red light coming from droplets of water higher in the sky, while droplets of water lower in the sky send violet light to the eye.

The Shape of the Rainbow
 All of the droplets of water along the arc shown in the figure are equivalent.   A rainbow would form a complete circle, not just an arc, if the ground didn't get in the way.

Understanding Rainbow Geometry

Rainbow
 Rainbows always face the observer.  As the observer moves, the rainbow moves. One can never get to the "pot of gold" at the end of the rainbow.

Double Rainbows
 The secondary rainbow displays colors in the reverse order. Looking below about 42 degrees, the sky is relatively bright, and acts like a mirror to the sunlight. Above 42 degrees, the water absorbs most of the sunlight, and the sky is darker.

Double Rainbows Explained
 One reflection in a primary rainbow   droplet. Two reflections in a secondary rainbow droplet.

Internal Reflection
 All rays reflect internally, but  the top three rays reflect only  a small percentage internally;  most energy leaves the prism.    The fourth and fifth rays are  reflected 100 % internally.

Internal Reflection and the Critical Angle
 Critical angle is 48 degrees. Any ray which strikes the surface from inside the water at an angle greater than 48 degrees will not escape the water.

The View from Below the Water
 Rays A, B, and C from the bottom of the pond are totally internally reflected.   Outside the 96- degree cone, the fish sees only light reflected from the bottom of the pond.

 A FishEye's View of the World (Excellent applet illustrating refraction)

Internal Reflections in Prisms

Prisms in Binoculars
 Magnifying power of binoculars is made larger by increasing the path length traveled between the two lenses.

Total Internal Reflection in Diamond
 The critical angle for diamond in air is 24.5 degrees

Internal Reflections in Diamond
 The critical angle for diamond in air is 24.5 degrees; any ray which strikes the surface on the inside at an angle of greater than 24.5 degrees will not escape the diamond.

Optical Fibers

Optical Fiber

Optical Fibers in Medicine
 Arthroscopic Surgery                              Bronchoscope                                            Colonoscope

Convex Lenses

Convex Lenses

The Convex Lens
as a Magnifier

Convex Lenses Used as Magnifiers

Concave Lenses

The De-Magnifier

Convex Lens is Inverse
of Concave Lens

Refraction
 Surface of water is like a collection of lenses which change shape.  Changing air densities explain why stars twinkle.

Image Formation
 Without angle-selectivity, light from all parts of the object overlap all parts of the wall. Pinhole in box, or a lense directs rays from one part of the object to only one point on the screen.   In bright light , the eyes' pupils becomes smaller, allowing sharper images to form.

Image Formation with Lenses
 If object is far from the lens (beyond) the focal point, a real inverted image is formed.

Film Projectors

Camera Film Image

Applets
 1.  Converging Lens Interactive Applet    2.  Diverging Lens Interactive Applet

Spherical Aberration
 Rays away from the center are not focused at    the focal point.

Chromatic Aberration
 Different colors refract by different  amounts.

Photoemission

Important Persons in Early 20th Century Physics

Solvay Conference, 1911
Einstein explained the
photoelectric effect by
assuming that
electromagnetic energy
(light) manifests itself as
quanta of energy--or,
"photons"--of energy hf:

 E = hf

f = frequency of light

Duality of Light
 Light acts like a wave when it's moving from one place to another, but when it interacts with matter, it acts like a particle.

Photocells in Garage Door Openers
 Light to photocell is interrupted, and the corresponding drop in photocurrent signals the motor to reverse.

Photocells in Movie Film
 Optical sound track is like a bar-code, but much more detailed.  Track modulates the intensity of the light at a frequency which is the same as the sound which was used to produced the track.