and Mirrors
-----------------------------------------------------
Joseph F. Alward, PhD
Department of Physics
University of the Pacific
| Reflection
of Light and Mirrors -----------------------------------------------------
Joseph F. Alward, PhD |
|
| Applets in this eLecture: |
Important Equations and Concepts
| Mirror Equation: 1/p + 1/q = 1/f
p = object distance |
Concave Mirror: Focal length f is positive (F is in front of mirror) ------------------------- Convex Mirror: Focal length f is negative (F is behind mirror) Images are always upright, and smaller |
Spherical Wave Fronts and Rays
 |
Pulsating sphere generates spherical wavefronts which are similar to those generated by a point source of light. The circles are two-dimensional cross sections of the spherical wavefronts, which are points of of same pressure. In the case of light, the wavefronts are points of same electric field. The wavelength l is the distance between fronts of the same phase. In the case of sound waves, this would be the distance between condensations or rarefactions; for light from a point source, l is the distance between consecutive positive maxima. |
Wave Fronts and Rays
 Near the source, the wavefronts are curved. |
 Far from the source, the wavefronts are almost planes. |
Applet
| Light shadows. From points and rods. |
Law of Reflection
 |
Angle of Reflection = Angle of Incidence
Angles are measured with respect to the
|
Reflection Law Example
| Example Problem:
180 - 120 - 25 = 35 90 - 35 = 55 |
Specular vs Diffuse Reflection
 
 |
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,
|
Plane Mirror Geometry
 |
Plane Mirror Geometry
 |
Virtual Images in Plane Mirrors
 If light energy doesn't flow from the image, the image is "virtual". |
 |
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 Rodriguez de Silva y Velasquez.
Is Venus looking at herself? |
Left-Right Reversal
 |
 The printing is reversed when viewed in a rear-view automobile mirror. |
Spherical Concave Mirrors
 |
 |
Paraxial Rays
 |
Paraxial Rays from Distant Object
The sun's image will appear at the focal point. Solar cookers. |
Solar Energy Farm
 Rays focused on oil-filled pipes which collect heat, make steam, propel generator turbines. |
Receivers at Focal Point of Mirrors
 Sandia Laboratory, New Mexico. |
Left: Sodium is heated, in turn heats
helium gas which drives an electrical generator. ------------------------------------------------------------- Below: Sound waves reflected off parabolic mirror focus at microphone.
|
Radiotelescope
 1000-foot diameter spherical radiotelescope at Arecibo, Puerto Rico, looks for 21-cm wavelength radio signals. |
Spherical Aberration
 "aberration": departure from the normal |
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. |
Paraxial Rays
 |
Rays Through Focal Point
 |
Radial Rays
 |
Concave Mirror: Upright Virtual Image
 |
Concave Mirror: Upright Virtual Image
 This is the the geometry which applies to the use of the makeup mirror. |
Concave Make-Up Mirror
|
 |
Three-Ray Analysis of Concave Mirror Geometry
 |
Concave Mirror Example
 |
Concave Mirror Example
 |
Applets
| 1.
Concave
Mirror 2. Diverging Mirror |
Heads Up Display
 |
Heads Up Display
 |
Convex Spherical Mirrors
 |
 |
Ray Geometry in Convex Mirror Analysis
 |
| Convex Mirror Applet |
Mirror Symbols
 |
f = focal length p = distance between object and mirror q = distance between image and mirror ho = height of object hi = height of image M = magnification = hi / ho |
Mirror Magnification Equation
 |
Triangles are similar:
ho / (-hi ) = do /
di |
The Mirror Equation
 |
Similar triangles: ho /(- hi) = (p - f) / f (1) Recall:
ho / hi = - p/ q
(2) |
Summary of Sign
Conventions
| If it's in front, it's positive: ------------------------------------------------------------------------
Concave mirrors: focal point is in front
(f is positive) |
Convex Mirror Example
| f = - 6 cm p = 48 cm q = ? ------------------------------------ 1/p + 1/q = 1/f
1/48 + 1/q = 1/(-6)
= -(-5.33 / 48) |
 (M.C. Eshcher) |
Where is the image? Is the image real, or virtual? ---------------------------------------------- Is the image upright, or inverted? ---------------------------------------------- Is the magnification (1/9) of the figure in the mirror reasonable?
(Hint: compare the head size |
Concave Mirror Example
 |
1/p + 1/q = 1/f
1/20 + 1/q = 1/10
= -(20/20) |
Convex Side Mirrors
 |
The Mirror Equation 1/p + 1/q = 1/f (1) -------------------------------- Convex: f is negative -------------------------------- Object distances are always positive for all types of mirrors. p is positive ------------------------------- 1/q= 1/f - 1/p (2) = neg - pos = negative q is negative |
Magnification Equation: M = -q / p (3) ------------------------------------ M = -(negative)/positive = positive Image is upright ----------------------------------- From (2), we see that the magnitude of 1/q is always larger than 1/p, so the magnitude of qis always smaller than p: M is always less than one for a convex mirror. |
The Hubble Mirror
 |
M is always less than one for a convex mirror. What type of mirror is the Hubble mirror? What is the person in the mirror pointing at? |
| Other mirror applets |
