1. Physics 7C, Lecture 3 Winter Quarter -- 2007 Light rays, Wavefronts, Optics, Lenses Professor Robin Erbacher 343 Phy/Geo erbacher@physics.ucdavis.edu

2. Announcements Course syllabus (policy, philosophy) on the web: http://physics7.ucdavis.edu Quizzes every other lecture, ~20 minutes each, average of 4 best = 45% (or 20)% of grade. Final on Monday, March 19 10:30 am. If you cannot make this we suggest 7C in a different quarter. Quiz #2 today, see calendar on web. Quiz #1 results posted yesterday. Turn off cell phones and pagers during lecture.

3. Wavefronts So far we have represented waves, including sound using 1 dimension. Even with waves that spread out-- wave fronts passing through slits-- we pick a direction and use 1 dimension. We will now also approximate electromagnetic waves (light) with a model in one dimension as well. When we discuss light waves and the way they diverge or converge in 2 and 3 dimensional space, we use wavefronts. Wavefronts are concentric spheres in 3-d and lines in 2-d. A wavefront represent points of equal phase (e.g. the crest of the wave). The ray shows the direction in which the wavefront is moving. Rays are perpendicular to wavefronts.

4. Circular, Spherical, Planar Circular (2-d) and spherical (3-d) wavefronts can be approximated by plane waves (flat) for sufficiently small samples and large distances.

5. Rays of Light A source of waves often sends out a wavefront in all directions, but many times we are interested only in one direction. Then we draw rays!

6. Law of Reflection Just as in our generic 1-d wave model, when light hits a boundary with a different “impedance”, some of the energy is reflected and some is transmitted. If the boundary is smooth on a scale smaller than a, we have specular reflection: a mirror ! When the light ray comes in at an angle: “The Law of Reflection”

7. Law of Reflection

8. Impedances: Index of Refraction When light hits a medium with different “impedance”, the light either speeds up or slows down. This impedance is called the Index of Refraction (n) : Tractor wheels on soft grass… Compare to Sound Waves!

9. The Law of Refraction Snell’s Law: If the light enters at an angle to the normal, as it passes from medium 1 having index n 1 to medium 2 having index n 2, the light rays will bend according to the Law of Refraction (Snell’s Law). PRS Question: How are the light rays bent if they come in normal (perpendicular) to the boundary? a) The light rays will bend along the surface of the boundary. b) The rays will reflect backward completely. c) The rays will refract (bend) 45° to the normal. d) The light will pass through the boundary unchanged.

10. The Law of Refraction Snell’s Law: If the light enters at an angle to the normal, as it passes from medium 1 having index n 1 to medium 2 having index n 2, the light rays will bend according to the Law of Refraction (Snell’s Law). What’s the incident angle from the normal on the curve? If the light rays are normal to the boundary, then no refraction.

11. Mirages: Index of Refraction Refraction of light in the same medium: Temperature changes toward the ground causes the index of refraction to vary.

12. Unless it’s “monochromatic”, light contains components in a range of wavelengths, corresponding to various visible colors. Recall: v = f, where v is the velocity of the wave in a medium. We also know that for light, v = c/n, so that n = c/ f. This means that light can be separated! Different wavelengths will experience different “impedence” or n, and according to Snell’s Law, will refract at different angles! Spectrum of Light: Prisms

13. Aside: Why is the Sky Blue? Sun has white light (many colors), but nitrogen and oxygen scatter short wavelengths more easily, the so-called BIV part of the spectrum. In mid-day, the path through the atmosphere is smaller, so less scattering, and more of the yellows come through. In the evening, path length is very large and the wavelengths that make it through are reds and oranges. The more particles, the better the sunset! (The more the polution.) Sunset on Aitutaki, Cook Islands

14. Tricky Sights What’s going on? We use ray traces to explain why the pencil looks broken! Water, glass, or other media bend light like lenses. Result: Things are not always how they appear! Why doesn’t the fish look worried?

15. Total Internal Reflection When light passes from a more-dense (n 1 ) to a less-dense (n 2 ) medium, as the angle of incidence increases, the refracted ray in the less dense medium bends more toward the normal until  2 =90 o. At this angle, called the critical angle  c, all of the light is internally reflected back into the medium. The greater the difference between indices of refraction, the small the critical angle. Example: Fiber Optics Example: Diamonds  c =25 o

16. Images Whether through water or in a mirror, we often see images of objects in specific locations. We can now calculate where we will see these images, and how big they will be. Ray Traces!

17. Thin Lenses Lenses bend rays twice: at the front and at the back. Thin lenses are idealized, so we only look at the net effect on rays. Thin lens equation: f = focal length (+ converging, - diverging) o = object-to-lens (+ if object in front of lens) i = lens-to-image distance (can be +/-) We can use ray traces or this equation to find both real and virtual images, as you will see in DL this week. Magnification: A lens has a particular magnification: the image height to the object height.

18. Convex Lenses Similar to a pair of prisms with the tips on the top and bottom (D/L) Bends parallel rays towards the axis. Focal length

19. Concave Lenses Similar to a pair of prisms with the tips near the axis where they meet. Bends parallel rays away from the axis.

20. Optometry The ability of our eyes to change focus is called accommodation. Our ciliary muscles change the shape of our lenses. The farthest object you can see is the “far point” and should be at ∞. The closest point is the “near point”, and should be greater around 25 cm. Presbyopia (elderly eyes) comes from the loss of accommodation with age, and happens to everyone. (Bi-focals!) Hyperopia comes from flat corneas, and myopia from over-curved corneas. Two lens systems: Contacts, plus eyes, Can often fix things. You will practice with multiple lenses in DL.

21. Seeing the Light? What kind of wave is a light wave? It’s a transverse excitation, perpendicular to the direction of wave propagation. What’s the medium that’s displaced as the wave propagates? Nothing! Light propagates via oscillating electric and magnetic fields! (more on this next week in Block 9…) The Enigmatic Ether!

22. Light: Visible, and Invisible The light we see is a small portion of the radiation that exists! Visible Light: 4.3-7.5 x 10 14 Hz Ultra Violet (UV) X-rays/   rays Infra Red IR  wave, AM/FM, TV frequency wavelength

23. Light: Visible, and Invisible The light we see is a small portion of the radiation that exists! Visible Light: 4.3-7.5 x 10 14 Hz Ultra Violet (UV) X-rays/   rays Infra Red IR  wave, AM/FM, TV frequency wavelength