Electromagnetic Waves

The Electromagnetic Spectrum

Our eyes are only able to see visible light. Night-vision goggles expand a person’s “sight” to include infrared waves.

The Electromagnetic Spectrum

Color and Frequency Different frequencies of light correspond to different colors. ROYGBIV is the list of colors in order of increasing frequency (decreasing wavelength)

Speed of Electromagnetic Waves All electromagnetic waves travel at the same speed: THE SPEED OF LIGHT (c) In a vacuum: 2.97792 x 108 m/s In air: 2.97709 x 108 m/s So for the most part, c = 3.00 x 108 m/s

Wave Equation c = f ∙ λ Remember v = f ∙ λ So…… for Electromagnetic Waves, c = f ∙ λ speed of light = frequency ∙ wavelength

Light – Wave or Particle? Throughout history, light has been described as both a particle and a wave. Current model incorporates aspects of BOTH particle and wave theories. For now, let’s focus on the wave model since it best suited for an introductory discussion of light.

OPTICS LASER LIGHT AMPLIFICATION of SIMULATED EMMISION OF RADIATION

Laser light vs. White light White light (like from the sun or from an incandescent light bulb) is composed of many different frequencies. Even light of a single frequency (color) has some light waves in phase and some out of phase. LASER light has light of a single frequency and the waves are in phase with each other.

Seeing Laser Light We cannot see laser beam through clean air or water. If we add something to the air or water to make it cloudy, we can see the beam because of scattering

Reflection Remember that when a wave meets a hard boundary, it is REFLECTED. On a smooth surface, like a mirror, we call it specular reflection. On a rough surface, like a piece of paper or table top, we call it diffuse reflection.

Law of Reflection Angle of incidence θi = Angle of reflection θr

Law of Reflection Still holds for diffuse reflection at each spot!

Application to Pool!

Ray Diagrams We can use ray diagrams to locate an image formed by a mirror with simple geometry. An image formed by rays that appear to come from behind the mirror is called a virtual image.

Curved (Spherical) Mirrors

Convex Mirrors Convex mirrors produce small, upright images when far away from object. Up close, the image gets more life-size and its still upright.

Concave Mirrors Concave mirrors produce small, inverted images when the object is far away. Up close, the image gets larger and becomes upright and REALLY LARGE

Focal Point Horizontal rays hitting a convex mirror reflect off as if they were coming from a point behind the mirror. This is called the focal point. f = R/2

Focal Point For a concave mirror, the focal point is where the horizontal rays would meet after reflecting

Terms Focal Length = f Image distance = di Object distance = do Image height = hi Object height = ho

Flipping of image on concave mirror Real image: an image formed by light rays that can be seen on a screen Virtual image: an image from which light rays appear to diverge, even though they are not actually focused there.

“L.O.S.T.” Summary for blue image of red arrow object Location - Orientation? - Size? - Type? Front or Behind Right-side-up or Larger or Smaller Real or Mirror? How far? Up-side-down? than object? Virtual?

Mathematical Relationships Focal length, object and image distances have a positive sign when on the mirror’s front side Focal length and image distances on the back side of a mirror have a negative sign.

Magnification For an image in front of a mirror, M is negative and the image is inverted. For an image behind the mirror, M is positive and the image is upright.

Spherical Aberration Aberration: defined by Webster’s dictionary as “a departure from the expected or proper course”. Spherical mirrors have an aberration. Not all rays focus in the same location. This is most notable for rays striking the outer edges of the mirror (away from principle axis). Result is that image from spherical mirror usually blurry.

Parabolic Radio Telescopes

White Light White light (comprised of all the colors together) can be separated by a prism. This is called dispersion

Additive Primary Colors of Light Adding red, blue and green light results in white light When added in varying proportions, they can form all of the colors of the spectrum

Secondary Colors of Light Red + Green = Yellow R + G = Y Red + Blue = Magenta R + B = M Blue + Green = Cyan B + G = C Since adding Red and Cyan is the same as adding Red + Blue + Green, Red and Cyan are said to be COMPLEMENTARY COLORS of each other

Complementary Colors of Light Red and Cyan Blue and Yellow Green and Magenta -because added together, they would make white light! R + C = R + (B + G) = W B + Y = B + (R + G) = W G + M = G + (B + R) = W

Principles of color addition have important applications to color television, color computer monitors and on-stage lighting at the theaters. Each of these applications involves the mixing or addition of colors of light to produce a desired appearance.

Why is the Sky Blue? Violet and Blue light is scattered the most by the atmosphere. Our eyes are not very sensitive to Violet light so we see the sky as Blue.

Color of objects Objects absorb some wavelengths of light and reflect other wavelengths of light. Under different lighting conditions, the color of objects may appear different.

Common Misconception The color of an object does not reside in the object itself. Rather, the color is in the light that shines upon the object and that ultimately becomes reflected or transmitted to our eyes. 

Pigments Pure pigments absorb a single frequency or color of light. The color of light absorbed by a pigment is merely the complimentary color of that pigment! Blue pigment absorbs Yellow light Yellow pigment absorbs Blue light Green pigment absorbs Magenta light Magenta pigment absorbs Green light Red “ Cyan Cyan “ Red

Why Does the Ocean Appear Blue? Red light is absorbed, so the reflected light from the water is Cyan

Questions: Magenta light shines on a piece of paper with yellow pigment. What color does the paper look? M – B = (R + B) – B = R Red!

Questions: 2. Yellow light shines on a piece of paper with red pigment. What color does the paper look? Y - C = (R + G) – (B + G) = R + G – G (no blue light to reflect) = R Red!

Questions: 3. Yellow light shines on a piece of paper with blue pigment. What color does it look?

Questions: 3. Yellow light shines on a piece of paper with blue pigment. What color does it look? Y – Y = ????? The absence of light is what we see as BLACK

Polarization How do polarized sunglasses reduce glare?

Polarization Most light is made up of transverse electromagnetic waves that are oscillating in random directions (unpolarized) Some materials can filter out all waves of light except for those lined up in a particular direction. This light would be said to be polarized.

Polarized Sunglasses Light that reflects off at glancing angles of the road, or water, or glass tends to be horizontally polarized. Polarized Sunglasses have an axis that is vertical so glare from horizontal surfaces is eliminated.

The Blue Sky is Polarized! In general, the sky is partially polarized tangential to a circle centered in the sun and maximum polarization is found at ninety degrees from it. Therefore, at noon when the sun is directly overhead, the sky will be polarized horizontally along the entire horizon.  http://www.atoptics.co.uk/fz1013.htm

A polarizing filter on a camera makes the sky look more blue…

Refraction As light travels from one medium to another, it changes speed. This change in speed results in a bending of the light ray. We say it is REFRACTED.

Reflection AND Refraction Sometimes, light is partially reflected and partially refracted. The Law of Reflection still holds.

Index of Refraction The ratio of the speed of light in a vacuum (c= 3.00 x 108 m/s) to the speed of light in a given material (v) is called the index of refraction (n) n = speed of light in a vacuum = c speed of light in a material v nair = 1.0003 ndiamond = 2.417 (slowed down by <½)

Snell’s Law n1sinθ1 = n2 sinθ2 Notice that when light is slowed down as it enters a material, it is refracted towards the normal. When it speeds up, it is refracted away from the normal.

Calculator Help Example 1.0003 sin 32°= 1.54 sin θ2 Make sure calculator set to degrees (not radians !) Know how to use sin and sin-1 functions. Example 1.0003 sin 32°= 1.54 sin θ2 -multiply 1.0003 times the sin 32 = .5300 -then divide by 1.54 to get .3442 -then take the sin-1 of .3442 to get 20.1°

Total Internal Reflection Light going from water to air Increase θ1 gradually Eventually reach a θCRITICAL where light is totally internally reflected As long as θ1 is > θCRITICAL you get TIF

Total Internal Reflection Applications: Reflectors Driveway markers Binoculars Fiber optics Fountains

Total Internal Reflection For any interface between two materials, there is a unique critical angle. Some materials have a critical angle that is not very large, so light becomes “trapped” inside the material. Diamond has a critical angle of about 25°. Light entering a diamond strikes many of its internal surfaces before striking one at less than 25° and emerging.

TIF in Diamonds

How to Find Critical Angle To find the critical angle of a material, set the angle of refraction to 90° So for light going from water to air: n1sinθ1 = n2 sinθ2 1.33 sinθ1 = 1.0003 sin 90 θ1 = 48.7 °

Lenses We know light passing from one material to another bends at the surface (refraction). What if we have a curved surface? Convex lens – thick in middle (also called converging lens) Concave lens – thin in middle (also called diverging lens)

Convex Lenses Light entering lens parallel to primary axis converges to focal point (Converging Lens!) + f

Concave Lens Light entering lens parallel to primary axis diverges as if coming from focal point. - f

Mathematical Relationships Same as for curved mirrors!

Two-Ray Diagrams To draw a ray diagram and locate the image, three rays can be drawn. (Need two)

Convex Lenses Ray diagrams can explain why image changes with object distance Object far away: inverted, small, real image Object closer, but still outside focal point: inverted, bigger, real image Object really close, inside focal point: upright, bigger, virtual image (-di)

Concave Lens No matter where object is placed, the image produced is virtual, upright and on same side of lens as focal point (- di)

Summing up Convex lenses have +f If do> f, then image is inverted, real and on other side of lens (+di) If do< f, then image is upright, virtual and on same side of lens (-di) Concave lenses have –f Images are always upright, virtual, smaller, and on same side of lens (-di)