Major Concepts in Physics Lecture 10.

1. Major Concepts in Physics Lecture 10. Prof Simon Catterall Office 309 Physics, x 5978 smc@physics.syr.edu http://physics/courses/PHY102.08Spring PHY102

2. Plan for today • Light. Ray approximation • Reflection and refraction. Snell’s law. • Mirrors, plane, convex and concave • Total internal reflection • Examples PHY102

3. Wavefronts, rays • As wave propagates in 2 or 3 dimensions set of wave crests is called wavefront • All points on wavefront are in phase • Often convenient to draw a vector perpendicular to wavefront showing direction of propagation – ray • Many problems involving light can be analyzed using these rays …. PHY102

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5. Wavefronts A set of points with equal phase is called a wavefront. PHY102

6. Ray approximation • Waves, wavefronts travel in straight lines and can be discussed in terms of rays when wavelength is much smaller than characteristic size of objects in system • Often happens for light. Geometric optics • It fails when diffraction/interference effects become important … PHY102

7. Huygens’s principle: At some time t, consider every point on a wavefront as a source of a new spherical wave. These wavelets move outward at the same speed as the original wave. At a later time t+t, each wavelet has a radius vt, where v is the speed of propagation of the wave. The wavefront at t+t is a surface tangent to the wavelets. PHY102

8. Reflection of Light When light is reflected from a smooth surface the rays incident at a given angle are reflected at the same angle. This is specular reflection. Understand using Huygens… PHY102

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10. Demo • Plane mirror PHY102

11. Reflection from a rough surface is called diffuse reflection. “Smooth” and “rough” are determined based on the wavelength of the incident rays. PHY102

12. The angle of incidence equals the angle of reflection. The incident ray, reflected ray, and normal all lie in the same plane. The incident ray and reflected ray are on opposite sides of the normal. PHY102

13. The light rays appear to come from behind the mirror. An image is virtual if the light rays from a point on the object are directed as if they diverged from a point on the image, even though the rays do not actually pass through the image point. Your eye focuses the diverging rays reflected by the mirror. PHY102

14. A ray parallel to the principle axis is reflected, and it appears to have come from point F, the focal point of the mirror. For a convex mirror, the focal point is on the axis and is located a distance 0.5R behind the mirror, where R is the radius of curvature. PHY102

15. Refraction • When light reaches interface between two media one generally finds • Reflected ray • Transmitted ray • Latter generally propagates in new direction. This is called refraction • Change in direction depends on index of refraction PHY102

16. Index of refraction n • Velocity of light in vacuum (air also) is c • Velocity of light in medium (say glass) is c/n • n is a pure number n>1 • Since c=lf  l/n smaller wavelength in material (note: frequency stays same) • Causes a wavefronts/rays to be bent PHY102

17. Demo • Refraction in block of glass. • Note: rays bent towards normal if entering higher n material away from normal if entering smaller n material PHY102

18. Fig. 23.19 PHY102

19. Snell’s Law where the subscripts refer to the two different media. The angles are measured from the normal. When going from high n to low n, the ray will bend away from the normal. PHY102

20. incident wave 1 n1 = 1.00; air surface n2 = 1.33; water 42° Transmitted wave Normal Example (text problem 23.11): Sunlight strikes the surface of a lake. A diver sees the Sun at an angle of 42.0° with respect to the vertical. What angle do the Sun’s rays in air make with the vertical? PHY102

21. Magical coffee cup PHY102

22. Refraction effects – inverted image PHY102

23. Total Internal Reflection The angle of incidence for when the angle of refraction is 90° is called the critical angle. PHY102

24. Demo – total internal reflection For angles of incidence greater than critical angle no transmitted ray! All light is reflected. Examples: glass tubes, optical fiber … PHY102

25. 2=90 n2 = 1.0; air Transmitted wave n1 = 1.77; sapphire surface 1 incident wave Normal Example (text problem 23.22): Calculate the critical angle for sapphire surrounded by air. PHY102