Physics 1502: Lecture 28 Today s Agenda Announcements: Midterm 2: Monday Nov. 16 Homework 08: due next Friday Optics Waves, Wavefronts, and Rays Reflection Index of Refraction 1
Waves, Wavefronts, and Rays Consider a light wave (not necessarily visible) whose E field is described by, This wave travels in the +x direction and has no dependence on y or z, i.e. it is a plane wave. 3-D Representation RAYS Wave Fronts EM wave at an interface What happens when light hits a surface of a material? Three Possibilities Reflected Refracted (transmitted) Absorbed incident refracted reflected MATERIAL 1 MATERIAL 2 2
θ i θ r x Lecture 4 Geometric Optics What happens to EM waves (usually light) in different materials? index of refraction, n. Restriction: waves whose wavelength is much shorter than the objects with which it interacts. Assume that light propagates in straight lines, called s. Our primary focus will be on the REFLECTION and REFRACTION of these s at the interface of two materials. incident refracted reflected MATERIAL 1 MATERIAL 2 Reflection The angle of incidence equals the angle of reflection θ i = θ r, where both angles are measured from the normal: Note also, that all s lie in the plane of incidence θ i θ r Why?» This law is quite general; we supply a limited justification when surface is a good conductor, Electric field lines are perpendicular to the conducting surface. The components of E parallel to the surface of the incident and reflected wave must cancel!! E i θ i E r θ r 3
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Index of Refraction The wave incident on an interface can not only reflect, but it can also propagate into the second material. Claim the speed of an electromagnetic wave is different in matter than it is in vacuum. Recall, from Maxwell s eqns in vacuum: How are Maxwell s eqns in matter different? ε 0 ε, µ 0 µ Therefore, the speed of light in matter is related to the speed of light in vacuum by: where n = index of refraction of the material: The index of refraction is frequency dependent: For example n blue > n red 6
Refraction How is the angle of refraction related to the angle of incidence? Unlike reflection, θ 1 cannot equal θ 2!!» n 1 n 2 v 1 v 2 but, the frequencies (f 1,f 2 ) must be the same the wavelengths must be different! Therefore, θ 2 must be different from θ 1!! θ 1 θ 2 n 1 n 2 λ 1 λ 2 7
From the last slide: Snell s Law λ 1 θ 1 L θ 1 n 1 θ 2 θ 2 θ 2 λ 2 θ 1 θ 2 n 2 The two triangles above each have hypotenuse L But, 8
Lecture 28, ACT 1 Which of the following diagrams could represent the passage of light from air through glass and back to air? (a) (b) (c) Lecture 28, ACT 1 Which of the following diagrams could represent the passage of light from air through glass and back to air? (a) (b) (c) 9
Lecture 28, ACT 2 Which of the following diagrams could represent the passage of light from air through glass and back to air? (a) (b) (c) (d) Prisms A prism does two things, 1. Bends light the same way at both entrance and exit interfaces. 2. Splits colours due to dispersion. Index of refraction 1.54 1.52 1.50 white light frequency ultraviolet absorption bands prism 10
Prisms Entering Exiting θ 1 θ 3 θ 4 θ 2 For air/glass interface, we use n(air)=1, n(glass)=n Prisms Overall Deflection θ 1 φ θ 2 θ 3 θ 4 At both deflections the amount of downward deflection depends on n (and the prism apex angle, φ). The overall downward deflection goes like, γ ~ A(φ) + B n Different colours will bend different amounts! 11
Lecture 28, ACT 3 White light is passed through a prism as shown. Since n(blue) > n(red), which colour will end up higher on the screen??? A) BLUE B) RED LIKE SO! In second rainbow pattern is reversed 12
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Total Internal Reflection Consider light moving from glass (n 1 =1.5) to air (n 2 =1.0) n 1 n 2 incident θ 1 θ r θ 2 refracted reflected GLASS AIR ie light is bent away from the normal. as θ 1 gets bigger, θ 2 gets bigger, but θ 2 can never get bigger than 90!! 2 In general, if sin θ 1 sin θ C (n 2 / n 1 ), we have NO refracted ; we have TOTAL INTERNAL REFLECTION. For example, light in water which is incident on an air surface with angle θ 1 > θ c = sin -1 (1.0/1.5) = 41.8 will be totally reflected. This property is the basis for the optical fibers used in communication. ACT 4: Critical Angle... An optical fiber is cladded by another dielectric. In case I this is water, with an index of refraction of 1.33, while in case II this is air with an index of refraction of 1.00. Compare the critical angles for total internal reflection in these two cases a) θ ci >θ cii b) θ ci =θ cii c) θ ci <θ cii Case I Case II θ c θ c water n =1.33 glass n =1.5 water n =1.33 air n =1.00 glass n =1.5 air n =1.00 14
The same two fibers are used to transmit light from a laser in one room to an experiment in another. Which makes a better fiber, the one in water (I) or the one in air (II)? a) Ι Water b) ΙΙ Air ACT 5: Fiber Optics Case I Case II θ c θ c water n =1.33 glass n =1.5 water n =1.33 air n =1.00 glass n =1.5 air n =1.00 Problem You have a prism that from the side forms a triangle of sides 2cm x 2cm x 2 2cm, and has an index of refraction of 1.5. It is arranged (in air) so that one 2cm side is parallel to the ground, and the other to the left. You direct a laser beam into the prism from the left. At the first interaction with the prism surface, all of the is transmitted into the prism. a) Draw a diagram indicating what happens to the at the second and third interaction with the prism surface. Include all reflected and transmitted s. Indicate the relevant angles. b) Repeat the problem for a prism that is arranged identically but submerged in water. 15
A) Prism in air Solution At the first interface θ=0 o, no deflection of initial light direction. At 2nd interface θ=45 o, from glas to air? Critical angle: sin(θ c )=1.0/1.5 => θ c = 41.8 o < 45 o Thus, at 2nd interface light undergoes total internal reflection At 3rd interface θ=0 o, again no deflection of the light beam B) Prism in water (n=1.33) At the first interface θ=0 o, the same situation. At 2nd interface now the critical angle: sin(θ c )=1.33/1.5 => θ c = 62 o > 45 o Now at 2nd interface some light is refracted out the prism n 1 sin(θ 1 ) = n 2 sin(θ 2 ) => at θ 2 = 52.9 o Some light is still reflected, as in A)! At 3rd interface θ=0 o, the same as A) 16