Refraction in 2 Dimensions Contents Two dimensions Whiteboard
Refraction in 2 Dimensions Contents: • Two dimensions • Whiteboard • Critical angle • Total internal reflection • Dispersion
Refraction in 2 dimensions Light hitting slower medium: Straight on = smaller wavelength Big Small TOC
Refraction in 2 dimensions Light hitting slower medium: Hits at an angle = smaller wavelength, bends Demo - laser TOC
Refraction in 2 dimensions Light hitting slower medium: Hits at an angle = smaller wavelength, bends TOC
Refraction in 2 dimensions Derivation Two rt triangles, l 1 = v 1 T, l 2 = v 2 T, co-hypotenicular TOC
Refraction in 2 dimensions n 1 = sin 2 = v 2 n 2 = sin 1 = v 1 n 1 = index of medium 1 1 = angle in medium 1 n 2 = index of medium 2 2 = angle in medium 2 Example - a laser hits glass at 23 o angle from air, what angle does it make with the bottom surface of the glass after entering? n = 1. 51 n = 1. 00 23 o ? ? ? n = 1. 51 TOC
Refraction in 2 dimensions Also: n 1 = sin 2 = v 2 n 2 = sin 1 = v 1 1 = angle in medium 1 (note where angle is) v 1 = velocity in medium 1 2 = angle in medium 2 v 2 = velocity in medium 2 TOC
Refraction in 2 dimensions 1|2|3|4 TOC
A beam of light makes an angle of 25 o with the perpendicular on the air side of a liquid, and 17 o below the liquid. What is the substance’s index of refraction? n 1 sin 1 = n 2 sin 2 n 1 = 1. 00, 1 = 25 o, 2 = 17 o 25 o n = ? ? 1. 45 n = 1. 00 17 o W
A ray of light has an incident angle of 12 o with the underside of an air-water interface, what is the refracted angle in the air? (n = 1. 33 for water, 1. 00 for air) n 1 sin 1 = n 2 sin 2 n 1 = 1. 33, 1 = 12 o, n 2 = 1. 00 ? ? n = 1. 33 16 o n = 1. 00 12 o W
What angle does a light ray that makes a 32 o angle with the bottom surface of an air-water interface make with the top side when it is in the air? (n = 1. 33 for water, 1. 00 for air) Tricky - is 32 o the incident angle? 32 o n 1 sin 1 = n 2 sin 2 n 1 = 1. 33, 1 = 90 -32 o, n 2 = 1. 00 Yaakk? ? W
Critical Angle From slow to fast Light bends over. When fast = 90 o, light does not leave water - total internal reflection Demo - fiber optic, light underwater TOC
What is the Critical angle for an air-water interface? n = 1. 00 θc n = 1. 33 n 1 sin 1 = n 2 sin 2 n 1 = 1. 33, c = ? ? , 2 = 90 o, n 2 = 1. 00 c = sin-1(1. 00 xsin(90 o)/1. 33) 48. 8 o W
What is the Critical angle for an water-diamond interface? Where does the critical angle occur? n = 1. 33 θc n = 2. 42 n 1 sin 1 = n 2 sin 2 n 1 = 2. 42, c = ? ? , 2 = 90 o, n 2 = 1. 33 c = sin-1(1. 33 xsin(90 o)/2. 42) 33. 3 o in the diamond W
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