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Physics 7E Prof. D. Casper Admin • Chapter 32 HW is due Thursday, 7 am • Discussion Thursday (Chapter 33) • Reading • Friday: Veterans’ Day! • Next Monday: Chapter 33.6 – 33.7 • Next Wednesday: Chapter 34.1 – 34.2 • Chapter 33 HW is due next Thursday (Nov. 17) Wave Fronts and the Ray Model A wave front is a set of adjacent points at which the phase of the wave is the same • Crests are wavefronts • Troughs are wavefronts too Rays are imaginary lines along the wave’s direction of travel For waves traveling in a homogeneous material, rays are straight lines normal to the wave fronts (At a boundary between materials, the direction of rays may change) Point source emitting spherically expanding wave fronts (crests) Reflection and Refraction Just as a wave on a string can be partially reflected and partially transmitted at a boundary, so can electromagnetic waves The transmitted part of the light wave is called “refraction” because unlike the one-dimensional wave on the string, it is bent into a different direction Law of Reflection Specular reflection (reflection from a smooth surface) obeys very simple laws: • Incident and reflected rays line in same plane with normal to surface • Angle of reflection = Angle of incidence • 𝜃𝑟 = 𝜃𝑎 Specular reflection Diffuse reflection Index of Refraction Light always moves at the same, fixed speed in vacuum: 𝑐 In a material, the speed of light can and will be different (smaller): 𝑣 The index of refraction 𝑛 specifies the speed of light in a given material: 𝑐 𝑣= 𝑛 𝑛 = 1 for vacuum, and 𝑛 > 1 for materials For air, 𝑛 = 1.00029, which we usually approximate as 𝑛 = 1 The frequency of waves is the same across a boundary; the wavelength changes: 𝜆vacuum 𝜆= 𝑛 Q33.1 When light passes from vacuum (index of refraction n = 1) into water (n = 1.333), A. the wavelength increases and the frequency is unchanged. B. the wavelength decreases and the frequency is unchanged. C. the wavelength is unchanged and the frequency increases. D. the wavelength is unchanged and the frequency decreases. E. both the wavelength and the frequency change. A33.1 When light passes from vacuum (index of refraction n = 1) into water (n = 1.333), A. the wavelength increases and the frequency is unchanged. B. the wavelength decreases and the frequency is unchanged. C. the wavelength is unchanged and the frequency increases. D. the wavelength is unchanged and the frequency decreases. E. both the wavelength and the frequency change. Law of Refraction (Snell’s Law) The law of refraction at a boundary depends on the indices of refraction of the two materials: 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2 Note the incident and refracted rays are also in the same plane as the normal The angles of incidence and reflection are measured from the normal Q33.2 Light passes from air (index of refraction n = 1) into water (n = 1.333). If the incident angle qa is in the range 0° < qa < 90°, A. the refracted angle is greater than the incident angle. B. the refracted angle is equal to the incident angle. C. the refracted angle is less than the incident angle. D. the answer depends on the specific value of qa . A33.2 Light passes from air (index of refraction n = 1) into water (n = 1.333). If the incident angle qa is in the range 0° < qa < 90°, A. the refracted angle is greater than the incident angle. B. the refracted angle is equal to the incident angle. C. the refracted angle is less than the incident angle. D. the answer depends on the specific value of qa . A Bent Ruler? Index of Refraction Index of Refraction varies for different materials Always 1 for vacuum and ~1 for gases Worth remembering • Water: 𝑛 = 1.333 • Glasses: 𝑛 = 1.5 − 1.8 No Refraction? Suppose we have light in glass (𝑛𝑎 = 1.55) incident on a boundary with water (𝑛𝑏 = 1.33) Because 𝑛𝑏 < 𝑛𝑎 , the angle 𝜃𝑏 > 𝜃𝑎 For some value 𝜃𝑎 = 𝜃𝑐𝑟𝑖𝑡 , 𝜃𝑏 = 90∘ For incident angles 𝜃𝑎 > 𝜃𝑐𝑟𝑖𝑡 , there is no angle 𝜃𝑏 which can satisfy the Law of Refraction, and there is no refracted ray We say total internal reflection occurs at the boundary Internal Reflection Internal reflection creates a striking effect underwater: the world above the water’s surface is compressed into a cone. Outside that cone, the water’s surface acts like a mirror Critical Angle The critical angle corresponds to an angle of refraction of 90∘ : 𝑛𝑎 sin 𝜃𝑐 = 𝑛𝑏 sin 90∘ = 𝑛𝑏 So 𝑛𝑏 sin 𝜃𝑐 = 𝑛𝑎 This angle only exists if 𝑛𝑎 > 𝑛𝑏 Total Internal Reflection Applications Critical Angle? The Critical Angle in total internal reflection occurs when incident light on a surface is … A. Refracted at 90∘ to the surface B. Reflected at 90∘ to the surface C. Refracted at 90∘ to the normal D. Reflected at 90∘ to the normal E. Totally absorbed Dispersion In real materials, the index of refraction depends on the wavelength (or frequency) This dependence is called “dispersion” and results in light of different colors being refracted differently Most noticeable when starting with a mixture of different colors (e.g. white light) Dispersion in a Prism Dispersion in Rainbows