Waves

1. Waves (part 4)

2. Reflection & Transmission Refraction Diffraction

3. Huygen’s Principle Every point on a wave front can be considered as a source of tiny wavelets that spread out in the forward direction at the speed of the wave itself. The new wave front is the envelope of all the wavelets – that is, the tangent to all of them.

4. Huygen’s Principle Consider Wave front AB

5. Huygen’s Principle To find the wave front A’B’ a short time t after it is at AB, tiny circles are drawn with radius r=vt. The centers are on AB. These circles represent Huygen’s (imaginary) “wavelets”.

6. Huygen’s Principle Tangent to all these wavelets, A’B’ is the new position of the wave front.

7. Huygen’s Principle • Reflection: • Because the speed of the waves does not change in a given medium, when we construct the wave fronts, we see: • Angle of Incidence = Angle of Reflection • “Law of Reflection”

8. Huygen’s Principle • Refraction: • Since frequency depends on the source, but speed depends on the medium, when a wave passes from medium 1 into medium 2: V1=λ1 V2λ2 • When we construct the wave fronts, we see they change direction.

9. Refraction of Light • If the speed of light is slower in medium A than in medium B, we say that medium A is “more optically dense” than medium B. • As light rays pass into a more optically dense medium, they are bent toward the normal. • As light rays pass into a less optically dense medium, they are bent away from the normal.

10. Snell’s Law for Refraction • For any two media: Sin θi= constant Sin θr Sin θi= n Sin θr n = “refractive index” (for a ray passing from a vacuum into a given medium)

11. Snell’s Law for Refraction • Using Huygen’s Principle we find: Sin θ1= c1 Sin θ2 c2 (for light traveling from medium 1 into medium 2) • We can further state that: n = c (c = speed of light in a vacuum) v (v = speed of light in the medium)

12. Total Internal Reflection • Light passes from a more optically dense medium into a less optically dense medium • Light ray is bent away from normal • Angle of refraction is larger than angle of incidence • Angle of incidence is so great that there is no refracted ray • All light is reflected back inside the medium

13. Critical Angle θc • Incident angle that causes the refracted ray to lie right along the boundary of a medium (angle of refraction = 90o) • Uses: • Fiber optics use glass fibers coated w/ glass of lower index of refraction • Total reflection prisms used in binoculars • Plants use total internal reflection to get light to cells

14. Wave Diffraction • bending of waves around edges of barriers • Angle through which a wave bends is greater, the larger the wavelength (for a given opening) • Waves spread out as they pass through openings • Wider opening: less diffraction • Most: slit width is comparable to incident wavelength

15. Wave Diffraction • Examples of Diffraction: • Sound waves bending around corners • Water waves spread out after passing through an opening between barrier islands • Fringes at shadow edges

16. Wave Diffraction & Interference • Laser light is diffracted through a narrow slit. • Light and dark areas • Slit acts as new point source, each producing circular wavefronts • Interference produces optical diffraction pattern