Major Concepts in Physics Lecture 11.

1. Major Concepts in Physics Lecture 11. Prof Simon Catterall Office 309 Physics, x 5978 smc@physics.syr.edu http://physics/courses/PHY102.08Spring PHY102

2. Anouncements • Exam 2 – Wednesday March 5 in class • Online: exam sample plus solutions, homework2 solutions, quiz 2 solutions • Material: everything from lecture 8-12 inclusive (thermal radiation, line spectra, color mixing, ray approx, mirrors, lenses, polarization) • Similar in format/style/grading to exam 1 • Review session in class on Monday March 3 PHY102

3. Plan for today • Recap basic features of geometrical optics: ray approx, reflection, refraction • Simple examples of refraction • Formation of images: diverging/converging mirrors/lenses. Inversion, magnification, real or virtual images • Simple examples and demos PHY102

4. Wavefronts, rays • If wavelength of wave much smaller than size of system – can use a ray approximation to calculate what happens to wave. • Rays show direction of propagation. At 900 to wavefront (locus of wave crests) • This approx neglects diffraction/interference effects • Often valid for light (l=500 nm) PHY102

5. Reflection and refraction • When light/wave passes from one medium to another eg airglass one finds • Reflected ray • Transmitted ray • Directions of these rays governed by simple laws • Reflection: angle of incidence=angle of reflection • Snell’s law: n1sin(q1)=n2sin(q1) PHY102

6. 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

7. 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

8. Total Internal Reflection For angles of incidence greater than the critical angle there is NO transmitted ray. Need n2<n1 PHY102

9. Refraction example – apparent depth • A kingfisher spies a fish which appears to be 1.0 m below the water surface. What is the true depth of the fish. Assume the refractive index of water is 4/3 PHY102

10. . PHY102

11. Solution Kingfisher sees not only vertical rays but rays at a non-zero angle. These are bent at water-air interface. Image formed by following bent rays backward. Use simple trig to relate true and refracted angles to real and apparent depth. Use Snell to relate in turn to refractive index. dapp/dreal=1/n=3/4 PHY102

12. Spherical mirrors • Two types – diverging and converging named according to whether rays diverge/converge after reflection • Possess a focal point – a point in space through which all rays, which were initially parallel to the symmetry axis of the mirror, pass after reflection • Focal point is at distance = radius of curvature / 2 PHY102

13. Diverging (convex) mirror PHY102

14. Points to note • For diverging mirror – focal point is behind the mirror • Corresponds to tracing the diverging rays back. Image is said to be virtual • Upright image • Locate image by drawing at least 2 rays – typically one that goes through focal point and one that passes through center of curvature PHY102

15. Drawn in green, red, and blue are the principal rays. • A ray parallel to the principal axis is reflected as if it came from the focal point. (green) • A ray along a radius is reflected back upon itself. (red) • A ray directed toward the focal point is reflected parallel to the principal axis. (blue) PHY102

16. Converging (concave) mirror • Image may be real or virtual. Real images correspond to points where physical rays cross. Can be projected on screen. • May be upright or inverted. PHY102

17. Real image Drawn in green, red, and blue are the principal rays. • A ray parallel to the principal axis is reflected through the focal point. (green) • A ray along a radius is reflected back upon itself. (red) • A ray along the direction from the focal point to the mirror is reflected parallel to the principal axis. (blue) PHY102

18. Converging mirror – virtual image PHY102

19. Demos • Diverging/converging mirrors … • Focal points – focusing infrared radiation and lighting matches …. • Spoons … PHY102

20. Lenses • Rays are bent not by reflection but by refraction • Thin lens approx – assume angle of bending proportional to distance of ray from center of lens PHY102

21. Diverging and converging lenses • Again all possess a focal point through which rays, initially parallel to principal axis, pass after transmission through lens • Also, any ray through center passes through without deviation • Allows us to draw ray diagrams as for mirrors • Images may be real, virtual, upright or inverted … PHY102

22. . PHY102

23. . PHY102

24. Demos • Simple lens behavior PHY102

25. Lens/Mirror equation • Can predict quantitatively the distances of images for both lens/mirrors using 1/p+1/q=1/f • p – distance of object from mirror/lens • q – distance of image from mirror/lens – q negative implies virtual image • f – focal length – positive for converging mirrors/lens. Negative for diverging. PHY102

26. Magnification • Use mirror/lens equation to find say q given p and f • Then use formula for magnification m=height object/height image m=-q/p Negative m means inverted image PHY102