c Earth Moon d Speed of Light 1 d = 240,000 mi c = v = 2d/t c = (2)(240,000 mi)/2.58 s t = 2.58 s c = 186,000 mi/s c = ? mi/s c = 3 x 108m/s
Earth d Speed of Light 2 How many round trips can a beam of light make around the earth in 1 second? 1, 10, 100, 1,000 ? d = 8,000 mi Distance traveled in 1s = 186,000 mi r = 4,000 mi 1 round trip = 2 π r = 2(3.14)(4,000 mi) v = 186,000 mi/s # of trips = 186,000 mi/ 2(3.14)(4,000 mi) C = 2 π r # of trips = approximately 8
c Sun Earth d Speed of Light 3 d = 93,000,000 mi c = v = d/t t = d/c c = 186,000 mi/s t = 93,000,000mi/186,000 mi/s t = ? s t = 500 s t = (500 s)(1 min/60 s) = 8.3 min t = ? min
Star Earth d Light Year 1 A light year (ly) is the distance light travels in 1 year t = 1 year v = 186,000 mi/s d = 1 ly = ? mi (1yr)(365d/yr)(24h/d)(3,600s/h) = 31,536,000 s d = v t = (186,000 mi/s)(31,536,000 s) d = 5,870,000,000,000 mi = 5.87 trillion miles 1 light year = 5.87 trillion miles
Star X Earth 100 ly Light Year 2 Light leaves star X in the year 2008 It arrives at Earth in the year 2108 We are all dead The light that we now observe from star X left the star in the year 1908.
Earth Planet X 10 ly ))))) c Earth Planet X 10 ly ))))) c Earth Planet X 10 ly v = 2 c Year 2006 Faster than the Speed of Light Spaceship leaves Earth traveling at 2c Year 2011 Spaceship arrives on Planet X. Light from takeoff is half way to Planet X. Year 2016 Light from takeoff arrives on Planet X. Space traveler watches his takeoff. To travel into the future you would have to travel faster than the speed of light.
v Crest Periodic Waves Periodic Wave Trough f = frequency f = waves/second 1wave/second = 1 Hertz λ = wavelength λ = distance crest to crest λ is measured in meters v = speed of the wave v is measured in m/s v = f If v is constant, = 1/f As f increases, decreases As increases, f decreases.
v Sound Waves What is the wavelength of middle C? f = 256 Hz Speed of sound in air ≈ 1,100 ft/s 335 m/s 750 mi/h v = f λ = v/f λ = 1100/256 λ = 4.30 ft If f is doubled f = 512 Hz, what is the wavelength of the wave? v = f λ = v/f λ = 1100/512 λ = 2.15 ft When f is doubled, the wavelength is half as great?
v Light waves The speed of light, c, is constant in a vacuum C = 186,000 mi/s 3.00 x 108 m/s This is the speed of all electromagnetic waves in a vacuum. What is the frequency of red light (λ = 6.5 x 10-7 m)? f = v/λ f = (3.00 x 108)/6.5 x 10-7) f = 4.6 x 1014 Hz f = 460,000,000,000,000 Hz f = 460 trillion Hz
WaveModel&Color v = f For red f is low, is long For blue f is high, is short
Color, frequency, and Wavelength λ is smaller f is higher λ is larger f is lower R O Y G B I V REEN LUE INDIGO IOLET ED RANGE EYYOW
Color Sensitivity of Human Eye The visible region of the spectrum is of course of particular interest to us. Figure 33-2 shows the relative sensitivity of the human eye to light of various wavelengths. The center of the visible region is about 555 nm, which produces the sensation that we call yellow-green The limits of this visible spectrum are not well defined because the eye-sensitivity curve approaches the zero-sensitivity line asymptotically at both long and short wavelengths. If we take the limits, arbitrarily, as the wavelengths at which eye sensitivity has dropped to 1% of its maximum value, these limits are about 430 and 690 nm; however, the eye can detect electromagnetic waves somewhat beyond these limits if they are intense enough.
Mixing of Colors Primary Colors of Light Red + Green = Yellow Red + Blue = Violet Red + Green + Blue = White
1. Light can be absorbed by matter 2. Light can be reflected by matter 3. Light can be transmitted through matter Light and Matter
Reflection 1 and Refraction
i r Reflection of Light i = r Irregular Reflection Regular Reflection Mirror Rough Surface
c Speed of Light in Matter vx < c vx c/vx = constant This constant is called n (index of refraction) c/vx= n For air vx approximately equals c Therefore, for air, n =1
The following substances are listed in alphabetical order. Arrange them in order of value of index of refraction. Remember, the higher the index of refraction, the slower the speed of light in that substance: Air Diamond Glass water. Index of Refraction of Various Materials • Air n = 1.0 • Water n = 1.3 • Glass n = 1.5 • Diamond n = 2.4
c = 3.0 x 108 m/s nwater = 1.3 nglass = 1.5 ndiamond = 2.4 Sample Problem #1 Determine the speed of light in each of these materials. nx = c/vx vx = c/nx vwater = 3.0 x 108 m/s/1.3 = 2.3 x 108 m/s vglass = 3.0 x 108 m/s/1.5 = 2.0 x 108 m/s vdiamond = 3.0 x 108 m/s/2.4 = 1.25 x 108 m/s
1 Refraction of Light Optical density of material 2 is greater than the optical density of material 1 2 1 > 2 Light will always bend toward the normal (dashed line).
1 2 Total Internal Reflection c At some angle, C , all light is reflected back into the material. Rays at angles > c are totally internally reflected The greater the index of refraction, n, the greater C .
Optical 1 Instruments
The Eye The image is formed on the retina. The image is inverted and real. As the object distance varies, the lens of the eye contracts or expands to change it’s focal length so that the image always forms on the retina.
Optical Instruments Eyepiece Objective For a telescope, the focal length of the objective lens is large. For a microscope, the focal length of the objective lens is small.
Eyepiece Objective Refracting Telescope do ≈ The focal length of the objective lens is large. The object is at infinity. 1/f = 1/do + 1/di 1/f = 1/ + 1/di 1/f = 1/di di ≈ f The image formed by the objective lens is at the focal point and is real. The image formed by the eyepiece is virtual and magnified.
Eyepiece Objective Microscope The focal length of the objective lens is small. The object is very close to the objective lens. The image formed by the objective lens is real. The image formed by the eyepiece is virtual and magnified.
Microscopes & Telescopes In a microscope, the focal length of the objective lens is small. Why? Because the object must be very close to the objective lens. In a telescope, the focal length of the objective lens is large. Why? Because the object is very far from the objective lens.