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optics Ch 7 - Lecture 2 Dr. Haya Alhummiany Phys 201 Refraction Refraction • • • Light rays may bend as they cross a boundary from one material to another, like from air to water. This bending of light rays is known as refraction. When a ray of light crosses from one material to another, the amount it bends depends on the difference in index of refraction between the two materials. Index of Refraction, n n = Index of Refraction c = Speed of light in vacuum v = Speed of light in medium Note that a large index of refraction corresponds to a relatively slow light speed in that medium. Index of refraction The ability of a material to bend rays of light is described by the index of refraction (n). Speed of Light & Refraction As you have already learned, light is extremely fast, about c = 3 108 m/s in a vacuum. Light, however, is slowed down by the presence of matter. The extent to which this occurs depends on what the light is traveling through. Light travels at about 3/4 of its vacuum speed (0.75 c ) in water and about 2/3 its vacuum speed (0.67 c ) in glass. The reason for this slowing is because when light strikes an atom it must interact with its electron cloud. If light travels from one medium to another, and if the speeds in these media differ, then light is subject to refraction (a changing of direction at the interface). Speed of Light & Refraction The speed at which light propagates through transparent materials, such as glass or air, is less than c. The ratio between c and the speed v at which light travels in a material is called the refractive index n of the material (n = c / v). For example, for visible light the refractive index of glass is typically around 1.5, meaning that light in glass travels at c / 1.5 ≈ 200000 km/s; the refractive index of air for visible light is 1.000293, so the speed of light in air is 299705 km/s or about 88 km/s slower than c. Reflection & Refraction At an interface between two media, both reflection and refraction can occur. The angles of incidence, reflection, and refraction are all measured with respect to the normal. The angles of incidence and reflection are always the same. If light speeds up upon entering a new medium, the angle of refraction, r , will be greater than the angle of incidence, as depicted on the left. If the light slows down in the new medium, r will be less than the angle of incidence, as shown on the right. normal normal r r Snell's law of refraction • Snell’s law is the relationship between the angles of incidence and refraction and the index of refraction of both materials. Angle of incidence (degrees) Angle of refraction (degrees) ni sin Qi = nr sin Qr Index of refraction of incident material Index of refraction of refractive material Calculate the angle of refraction • A ray of light traveling through air is incident on a smooth surface of water at an angle of 30° to the normal. • Calculate the angle of refraction for the ray as it enters the water. Calculate the angle of refraction • • • • • • • • • • • 1) You are asked for the angle of refraction. 2) You are told the ray goes from air into water at 30 degrees. 3) Snell’s law: ni sin(θi) = nr sin(θr) ni = 1.00 (air), nr = 1.33 (water) 4) Apply Snell’s law to find θr. 1.00sin(30°) = 1.33 sin(θr) sin(θr) = 0.5 ÷ 1.33 = 0.376 Use the inverse sine function to find the angle that has a sine of 0.376. θr = sin-1(0.376) = 22° Critical Angle nr The incident angle that causes the refracted ray to skim right along the boundary of a substance is known as the critical angle, c. The critical angle is the angle of incidence that produces an angle of refraction of 90º. If the angle of incidence exceeds the critical angle, the ray is completely reflected and does not enter the new medium. A critical angle only exists when light is attempting to penetrate a medium of higher optical density than it is currently traveling in. ni c From Snell, n1 sinc = n2 sin 90 Since sin 90 = 1, we have n1 sinc = n2 and the critical angle is c = sin-1 nr ni Critical Angle Sample Problem Calculate the critical angle for the diamond-air boundary. Refer to the Index of Refraction chart for the information. c = sin-1 (nr / ni) air diamond c = sin-1 (1 / 2.42) = 24.4 Any light shone on this boundary beyond this angle will be reflected back into the diamond.