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Lesson 8 November 17 th, 2010

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The phenomenon of refraction had been observed for centuries, but it was not until 1621 that its cause was stated mathematically.

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Willebrord Snell (1591–1626) was a Dutch astronomer and mathematician who is credited with identifying the exact relationship between the angle of incidence and the angle of refraction.

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Snell’s law is a formula that uses values for the index of refraction to calculate the new angle that a ray will take as a beam of light strikes the interface between two media.

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If you call the indices of refraction of the two media n 1 and n 2 and call the angles of incidence and the angle of refraction θ 1 and θ 2, then the formula for Snell’s law is: n 1 sinθ 1 = n 2 sinθ 2

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When light passes from air into water at an angle of 60° from the normal, what is the angle of refraction? GIndex of refraction of air n 1 = 1.00 Index of refraction of water n 2 = 1.33 Angle of incidence Ѳ 1 = 60° S sinθ 2 = 1.00 x sin60° 1.33 sinθ 2 = 0.6511 θ 2 = 40.62° R Angle of refraction = Ѳ 2 PTherefore, the angle of refraction is 41 degrees. A n 1 sinθ 1 = n 2 sinθ 2 sinθ 2 = n 1 sinθ 1 n 2

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In an experiment, a block of cubic zirconium is placed in water. A laser beam is passed from the water through the cubic zirconium. The angle of incidence is 50°, and the angle of refraction is 27°. What is the index of refraction of the cubic zirconium? GIndex of refraction is 1.33 Angle incidence Ѳ 1 = 50° Angle of refraction Ѳ 1 = 27° S n 2 = 1.33 x sin 50° sin 27° = 2.244 RIndex of refraction = n 2 PTherefore, the index of refraction of the cubic zirconium is 2.2 A n 1 sinθ 1 = n 2 sinθ 2 n 2 = n 1 sin Ѳ 1 sin Ѳ 2

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1. When light passes from air into water at an angle of 30° from the normal, what is the angle of refraction? 2. When light passes from water into diamond at an angle of 45° from the normal, what is the angle of refraction? 3. The refractive index of the lens in a human eye is 1.41. If a ray of light goes from the air into the lens at an angle of 55.0°, what is the angle of refraction?

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1. A ray of light approaches a jar of honey at an angle of 30.0°. If the angle of refraction is 19.5°, what is the refractive index of honey? 2. A block of amber is placed in water, and a laser beam travels from the water through the amber. The angle of incidence is 35° while the angle of refraction is 24°. What is the index of refraction of amber? 3. A red laser beam travels from flint glass into lemon oil. The angle of incidence is 40.0° and the angle of refraction is 44.4°. What is the refractive index of lemon oil?

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Sometimes, such as in the case of fibre optics, light does not pass from one medium to another but stays within the medium.

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In total internal reflection, light reflects completely off the inside wall of a denser medium (higher index of refraction) rather than passing through the wall into a less dense medium (lower index of refraction).

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Recall that when light passes from a denser material, such as water, into a less dense medium, such as air, the light refracts away from the normal.

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As the angle of incidence increases, the angle of refraction increases. At a certain angle, called the critical angle, the refracted ray of light follows a path exactly along the surface of the water. Even though the light refracts, it does not leave the water. In a way, the light is “trapped” inside the water

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When light crosses a boundary between materials with different indices, the light beam will be partially refracted at the boundary surface, and partially reflected.

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Both total internal reflection and refraction play a role in forming a mirage. A mirage is an image of a distant object produced as light refracts through air of different densities.

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Since the light rays pass through layers of air with progressively lower indices of refraction, eventually the light is totally internally reflected.

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