26 notes Cutnell student copy The refraction of light_ Lenses and optical instruments (1).docx

26 notes Cutnell student copy The refraction of light_ Lenses and optical instruments (1).docx

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Chapter 26 The refraction of light: Lenses and optical instruments 26.1 INDEX OF REFRACTION How fast a wave moves depends on the material it is traveling through. Sound waves travel faster through many solid materials whereas light travels slower. How fast it travels is dependent on its index of refraction. A. The Index of Refraction of a material is the ratio of the speed of light c in a vacuum to the speed of v of light in the material. B. Equation for Index of Refraction n=c/v n= index of refraction (found on page 784 of your book) c= speed of light in a vacuum 299792458 m /s (2.9979 x10 8 m/s or 3.00 x10 8 m/s) v= velocity of light in the new material C. Example problems 1. The index of refraction for light in air is 1.0003 . What is the speed of light in air? 1.0003= 2.9979 x 10 8 m/s v v = 2.9979 x 10 8 m/s 1.0003 2.997 x 10 8 m/s = v (speed of light in air) In both mediums if we only go to 3 sig figs we can say the speed of light is 3.00 x 10 8 m/s 2.(1) What is the speed of light in Carbon tetrachloride? n= 1.461 index of refraction (found on page 784 of your book) n=c/v 1.461= 2.9979x 10 8 m/s v v = 2.9979 x 10 8 m/s 1.461 v = 2.062 x 10 8 m/s 3.(2) Find the ratio of the speed of light in diamond to the speed of light in crown glass.
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v diamond (n=c/v) diamond v glass v diamond =c/n diamond c/n diamond c/n glass 1/n diamond (n diamond ) (n glass ) 1/n glass (n diamond ) (n glass ) n glass n diamond 1.523 2.419 .6296 4. Find the ratio of the speed of light in fused quartz to the speed of light in ice. v fused quartz (n=c/v) diamond v ice v diamond =c/n diamond c/n fused quartz c/n ice n ice n fused quartz 1.309 1.458 .8978 5.(3) The frequency of a light wave is the same when the light travels in diamond as it is when it travels in crown glass. Find the ratio of the wavelength of the light in diamond to that in crown glass. ` λ diamond v=f λ λ glass v/f ¿ λ c/nf diamond (v=c/n) diamond c/nf glass v/f diamond =c/nf diamond Since the frequency and c is the same in both mediums it can be canceled out 1/n diamond (n diamond ) (n glass ) 1/n glass (n diamond ) (n glass )
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n glass n diamond 1.523 2.419 .6296 6. The frequency of a light wave is the same when the light travels in benzene as it is when it travels in carbon disulfide. Find the ratio of the wavelength of the light in benzene to that in carbon disulfide. ` λ benzene v=f λ λ carbon disulfide v/f ¿ λ c/nf b (v=c/n) diamond c/nf cd v/f diamond =c/nf diamond Since the frequency and c is the same in both mediums it can be canceled out n cd n b 1.632 1.501 1.087 7(4). Light has a wavelength of 390.0 nm and a frequency of 7.683 x 10 14 Hz when traveling through a certain substance. What substance from Table 26.1 could this be? v=f λ v= 5.24x10 14 Hz• 390.0 x 10 -9 v = 2.996 x 10 8 m/s n = c/v n = 2.998 x 10 8 m/s /2.996 x 10 8 m/s n= 1.00054 so it is carbon dioxide 8. Light has a wavelength of 420.0 nm and a frequency of 5.24 x 10 14 Hz when traveling through a certain substance. What substance from Table 26.1 could this be?
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  • Winter '19
  • Rene Bishop
  • refractive index, Total internal reflection, Geometrical optics

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