Lecture 33 reflection and refraction
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This document provides an introduction to geometric optics and concepts of reflection and refraction of light. It discusses how light rays interact with surfaces and change direction at boundaries between different optical media based on Snell's law. Total internal reflection is described, in which light reflecting back into the original medium if the angle of incidence is greater than the critical angle. Applications like fiber optics and mirages are discussed. A simple model is provided of light propagation through materials involving absorption and re-emission of photons by atoms.
Lecture 33 reflection and refraction
- 1. Lecture 33 Reflection and refraction.
- 2. Introduction to geometric optics Select an object of your choice (table, book, coin, neighbor’s head). Think about and discuss: • what it means to “see it” → EM waves (light) from lamps hit surface and are reflected. → Waves propagate spherically in all directions from object. → Your eye is sensitive to light • how you perceive the position of that object → brain “traces back” to where the light comes from. → 3D perception comes from brain comparing images from each eye.
- 3. Light rays = Geometrical abstraction that allows us to work with the direction that an E/B wave travels Instead of drawing E/B fields, we draw a “ray” Ray : a line in the direction along which light energy is traveling
- 4. Ray Model of Light • • • Light travels through a transparent medium in straight lines at a speed v =c /n (n = index of refraction) Light rays do not interact with each other A light ray continues forever unless it interacts with matter Interactions light/matter: • at an interface between two media → reflected and refracted • within a medium, light can be scattered or absorbed medium 1 reflection scattering medium 2 refraction absorption
- 5. ACT: Vertical slit You have a point source of light behind a wall with a 5 cm tall vertical slit aperture. A screen is placed 2 m in front of the wall. How tall is the slit you see on the screen? A. 5 cm B. 10 cm Light source C. 15 cm Image of point A A B ϕ 5cm x Image of point B 1m 5 cm x = 1m 3m 2m screen x = 15 cm
- 6. Two types of reflection specular reflection smooth surface e.g. mirrors diffuse reflection rough surface e.g. screens
- 7. Mirror reflection θi θr mirror • Incident angle = reflected angle • Always draw line that is “normal” (90°) to mirror – calculate angles with respect to this normal DEMO: Mirrors
- 8. Image reflected on a plane mirror A book is in front of a plane mirror. If you see it through the mirror, where does it appear to be? All the reflected rays seem to be coming from here! No rays really pass behind the mirror. This is a virtual image.
- 9. How to find the image • Draw two rays (one of them the normal to the surface, it’s a trivial one) • Draw reflected rays. • Extrapolate rays until they intersect. Plane mirror: s = -s’ s’ s s : location of the object Positive in front of mirror s’: location of the image Negative behind mirror
- 10. EM waves not in vacuum Phys 221: E field inside a material is characterized by dielectric constant κ or the dielectric permittivity ε = κε 0 Similarly: B field inside a material is characterized by relative permeability κm or the permeability µ = κ m µ0 (often κ m : 1) EM wave speed in a dielectric: v = 1 εµ = c κκ m c = n n = κκ m (>1 always ) Refraction index
- 11. Refraction Fact: Light changes direction when it crosses a boundary Reason: Speed of light is different in both media – At boundary, part of wavefront is in slower media – Travels shorter distance in ∆t slower
- 12. Snell’s law na sin θa = nb sin θb Angles defined with respect to normal
- 13. ACT: Angle of refraction I If n1 > n2 , which direction does the ray go? n1 DEMO: Refraction air/plastic n1 sin θ1 = n2 sin θ2 n1 sin θ1 > sin θ1 n2 θ2 > θ1 sin θ2 = n2 A B C ⇒ Remember: angles defined with respect to normal!
- 14. ACT: Angle of refraction II When it re-emerges into medium 1, the direction of the ray is: n1 n1 sin θ1 = n2 sin θ2 = n1 sin θ1′ θ1 θ2 θ1 = θ1′ n2 θ2 A B θ1′ C n1 It comes out exactly parallel to the original ray. DEMO: Refraction air/plastic/air
- 15. In-class example: Refraction A ray of light strikes the interface between air and an unknown substance at an angle θ1 = 75° from the normal to the surface. The refracted beam makes an angle θ2 = 30° from the normal. What is the index of refraction of this substance? A. 2.5 75° 75° B. 1.9 C. 1.3 30° air X D. 1.0 E. 0.50 Impossible, n ≥ 1 = 1.0 nair sin 75° = nX sin30° nX = sin 75° = 1.9 sin30°
- 16. Total internal reflection As light goes to a medium with lower n, the angle from the normal increases (θ1 < θ2): θ1 n1 n2 < n1 θ2 θ1 θ2 θ1c θ1 θ2 If θ1 is large enough, θ2 = 90° !! Beyond this angle, there is no more refraction, only reflection. DEMO: Total internal reflection
- 17. Critical angle =1 n1 sin θ1c = n2 sin 90° n2 θ1c = sin n 1 −1 ÷ ÷ θ1c n1 n2 < n1 θ2 = 90°
- 18. Fiber optics cladding core Both cladding and core are glass such that ncore > ncladding Light internally reflects within the inner glass fiber – no refracted ray going outside – minimal light loss DEMO: Water tank. Fiber optics
- 19. Road mirages Hot air → lower density → lower n High n Total internal reflection Low n Hot road Image of sky on the road (that brain interprets as water to explain “reflection”)
- 20. Light through matter: a simple model What does really happen when light travels through matter? It depends on how you want to think about it. atom You can say that the photons occasionally interact with atoms in a dielectric, being absorbed and re-emitted, and that this only appears to slow them down. Here, the photons travel at “c”. v=c v=c absorb & re-emit with some phase delay Or you can say that the wave that propagates through the solid is a combination of a photon and virtual excitations of the atoms of the solid. This wave travels with v < c.
- 21. What defines a color? So the atom oscillates with the frequency of the radiation and then re-emits. → Frequency remains the same → Wavelength changes n1 v1 c λ1 = = f n1f n2 < n1 v2 c λ2 = = > λ1 f n2f “Color” correspond to a fixed frequency. The wavelength depends on the medium.