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The Refraction of Light : Notes/W.S.-10 When waves enter a different medium, they may speed up or slow down. The direction of the waves will then change. This change in direction is called refraction. The refracted beam bends towards or away from the normal, depending on whether the beam slows down or speeds up. For example, when light moves from air to water, it slows down and the light bends towards the normal. air water Using geometry, we can derive an important formula. The incident and refracted wave fronts are shown below. incident wavelength angle of incidence i a angle of refraction R b refracted wavelength In the diagram above, the light wave slows down so that the wavelength decreases. Therefore, we have: λ incident ab = sin ( i) and λ refracted ab = sin ( R ) Since the frequency doesn't change, we also have: vi vR = λi λR The above equations combine to give Snell's Law for light traveling from air to a more dense medium. sin(i) vi = =n sin(R) vR The ratio of the velocity of light in air to the velocity of light in the dense medium is called the index of refraction. It is given by the symbol n. For a light beam traveling from the dense medium to air, Snell's Law becomes: sin(i) 1 = sin(R) n Problems: 1)a) The speed of light in a vacuum (or air) is 3.00x108 m/s. When light enters water from the air, it slows down to 2.26x108 m/s. Find the index of refraction for water. b) If the angle of incidence (i) equals 38.0°, find the angle of refraction. i air water R 2)a) An incident light ray enters water from the air. If the wavelength of the light in air is 5.0x10-7 m, find the frequency. (use v = f⋅ λ ) b) Find the wavelength of the refracted beam. c) Find the frequency of the refracted beam. 3) If the index of refraction (n) for a substance is equal to 1.5, what will the speed of light in that substance be? 4) The index of refraction for diamond is 2.42. Fill in the blanks. angle of incidence i angle of refraction R 25.0° ____ 56.0° ____ ____ 15.0° ____ 0.0° 5) The angle of incidence i equals 32.0°, and the angle of refraction R is found to be 22.0° for a certain type of plastic. i) Find the index of refraction. ii) Find the velocity of light in the plastic. 6) If a light ray enters the air from water, the ray bends away from the normal as shown below. Find the angle of refraction R. air R water 28.0 7) Draw a picture to show what happens to the light ray as it goes through the pane of glass. (use a pencil and ruler) ray air glass air Answers: 1)a) 1.33, b) 27.6°, 2)a) 6.0x1014 Hz, b) 3.8x10-7 m, c) 6.0x10 14 Hz, 3) 2.0x108 m/s, 4) 10.1, 38.8, 20.0, 0.0, 5)i) 1.41, ii) 2.12x10 8 m/s, 6) 38.6°, 7) ray air glass air