Reflection and Refraction

1. Reflection and Refraction

2. Reflection Reflection occurs when light bounces off a surface. There are two types of reflection Specular reflection Off a shiny surface Diffuse reflection Off a rough surface

4. Ray tracing Ray tracing is a method of constructing an image using the model of light as a ray. We use ray tracing to construct optical images produced by mirrors and lenses. Ray tracing lets us describe what happens to the light as it interacts with a medium

5. Types of mirrors Plane mirrors Spherical mirrors

6. The Law of Reflection

7. Law of Reflection The angle of incidence of reflected light equals the angle of reflection. θR = θI Note that angles are measured relative to a normal to the mirror surface.

8. Optical images • Nature • real (converging rays) • virtual (diverging rays) • Orientation • upright • inverted • Size • true • enlarged • reduced

9. Ray tracing: plane mirror • Construct the image using two rays. Plus side Minus side Extend reflected rays behind mirror -5 cm 5 cm object image Reflected rays Are diverging Upright (virtual) Same size

11. The focalpoint is where the rays intersect! Rays parallel to the principal axis all pass through the focus for a Spherical concave mirror. Going from concave to convex the focal point stays on the concave side of the mirror!

12. r f C is the center of the sphere r is the radius of curvature F is the focal length of the mirror The focal length is always ½ of the radius!

13. θ θ θ Law of Reflection still works even on a curved surface (just like a rough surface)

15. Ray tracing: spherical concave mirror • The three “principal rays” to construct an image for a spherical concave mirror are • the p-ray, which travels parallel to the principal axis, then reflects through focus. • the f-ray, which travels through focus, then reflects back parallel to the principal axis. • the c-ray, which travels through center, then reflects back through center. • You must draw two of the three principal rays to construct an image.

16. p ray c ray F ray Construct the image for an object located outside the center of curvature. It is only necessary to draw 2 of the threeprincipal rays! Real image, inverted image, reduced image

17. p ray F ray Construct the image for an object located at the center of curvature. Name the image. Real image, inverted image, true image

18. c ray p ray f ray Real, Inverted, Enlarged Image

19. p ray c ray Construct the image for an object located at the focus. No image

20. f ray p ray c ray Construct the image for an object located inside the focus. Name the image. Virtual, Upright, Enlarged Image

21. (remember to right-click anywhere to pause) Object is at “C” Object and image meet! (As object moves toward mirror, image moves away)

22. Object is between “C” and “F”

23. Object is between “F” and mirror

24. Side-by-side comparison (remember to right-click anywhere to pause)

25. What’s the difference between a REAL and a VIRTUAL image?

26. What’s the difference between a REAL and a VIRTUAL image? A REAL image is on the SAME SIDE of the mirror as the object making the image. The Mirage demo creates a real image. Usually you need to project the REAL image onto a screen so you can see it. Like Alice in Wonderland objects not in the mirror (in Wonderland) are REAL or in the REAL world.

27. What’s the difference between a REAL and a VIRTUAL image? A VIRTUAL image we trace the rays back to a point where the rays appear to diverge. The image appears to be on the opposite side of the reflective surfac

28. Mirror equations • 1/si + 1/so = 1/f • si: image distance • so: object distance • f: focal length • M = hi/ho = -si/so • hi: image height • ho: object height • M: magnification

29. Sign conventions • Focal length (f) • Positive for CONCAVE mirrors • Negative for CONVEX mirrors • Magnification (M) • Positive for UPRIGHT images • Negative for INVERTED images • ENLARGED when M > 1 • REDUCED when M < 1 • Image Distance • si is POSITIVE for real images • si is NEGATIVE for virtual images

30. Refraction The bending of light rays

31. Refraction Formulas • Index of Refraction n = index of refraction v = speed of light in material c = speed of light in a vacuum

32. Formulas • Snell’s Law ni sin i= nr sin r i= angle of incidence ni = index of refraction for incident medium r = angle of refraction nr = index of refraction for refracting medium

33. Sample Problem The speed of light in plastic is 2.00 x 108 m/s. What is the index of refraction of plastic? n = ? v = 2.00 x 108m/s c = 3.00 x 108 m/s n = 3.00 x 108 m/s / 2.00 x 108m/s n = 1.5

34. Notes – Refraction/Snell’s Law • When light passes from one medium into another, • o   part of the incident light is reflected at the boundary and • o   the remainder passes into the new medium • -if the ray enters the new medium at an angle (other than perpendicular), the ray bends as it enters.

35. Sample Problem A ray of light traveling through air is incident upon a sheet of crown glass at an angle of 30o. What is the angle of refraction? ni sin i = nr sin r ni = 1.00 i = 30o nr = 1.52 (1.00)(sin 30o)= (1.52)(sin r) r = ?? 0.500 = sin r 1.52 r = 19.2o

36. Critical Angle When light passes from one material into a second material where the index of refraction is less (say, from water into air) light bends away from the normal. At a particular incident angle, the angle of refraction will be 90o, and the refracted ray will skim the surface. The angle of incidence at which this occurs is called the critical angle.

37. Sample Problem • Find the critical angle for diamond. ni = 2.42 (diamond) ni sin i = nr sin r c = ? nr = 1.00 (vacuum) r= 90o (2.42)(sin c) = (1.00)(sin 90o) c = 24.4o

38. Normal (90o) incident ray θi θr θr θi

39. The arrangement shown at the left is thicker in the middle and convergesthe light. The arrangement at the right, however, isthinner in the middle than at the edges; it diverges light

40. Converging, because the rays intersect (converge) 30-2

41. Diverging, because the rays move away from each other (diverge) 30-2

42. Convex Lenses: The lens below is a convex lens – also known as a converging lens.

43. The lens below is a concave lens, also known as a diverging lens.

44. The Thin Lens Equation The thin lens equations are the same as the mirror equations. However, there are different sign conventions that go along with using the equation for lenses.

45. For converging lenses • f is positive • do is positive • di is positive for real images an negative for virtual images • M is negative for real images and positive for virtual images • hi is negative for real images and positive for virtual images

46. For diverging lenses • f is negative • do is positive • di is negative • M is positive and < 1 • hi is positive and < ho