Chapter 25. Mirrors and the Reflection of Light

1. Chapter 25. Mirrors and the Reflection of Light Our everyday experience that light travels in straight lines is the basis of the ray model of light. Ray optics apply to a variety of situations, including mirrors, lenses, and shiny spoons. Chapter Goal: To understand and apply the ray model of light.

2. Models of Light • The wave model: under many circumstances, light exhibits the same behavior as sound or water waves. We used the wave model in Chapter 24. • The ray model: The properties of prisms, mirrors, and lenses are best understood in terms of light rays. The ray model is the basis of ray optics, which we shall study in Chapters 25 and 26. • The photon model: In the quantum world, light behaves like neither a wave nor a particle. Instead, light consists of photons that have both wave-like and particle-like properties. This is the quantum theory of light.

3. The Ray Model – A beam of sunshine or a laser is a good approximation of a light ray, although made up of many parallel rays or a laser

4. 25.1 Wave Fronts and Rays A hemispherical view of a sound wave emitted by a pulsating sphere. The rays are perpendicular to the wave fronts.

5. 25.1 Wave Fronts and Rays At large distances from the source, the wave fronts become less and less curved.

6. The Ray Model • Light rays travel in straight lines. • Light rays can cross without interacting. • An object is a source of an infinite number of light rays. Rays originate from every point and each point sends rays in all directions. • Both self-luminous objects and reflective objects are the source of light rays

7. The Ray Model • To simplify, we usually draw only a few rays from the object.

8. In specular reflection, the reflected rays are parallel to each other.

9. Law of Reflection • The incident ray and the reflected ray are in the same plane normal (perpendicular) to the surface, and • The angle of reflection equals the angle of incidence: θr = θi

10. 25.2 The Reflection of Light LAW OF REFLECTION The incident ray, the reflected ray, and the normal to the surface all lie in the same plane, and the angle of incidence equals the angle of reflection.

11. 25.3 The Formation of Images by a Plane Mirror • The person’s right hand becomes • the image’s left hand. • The image has three properties: • It is upright. • It is the same size as you are. • The image is as far behind the • mirror are you are in front of it.

12. The Plane Mirror Consider P, a source of rays which reflect from a mirror. The reflected rays appear to emanate from P', the same distance behind the mirror as P is in front of the mirror.

13. 25.3 The Formation of Images by a Plane Mirror A ray of light from the top of the chess piece reflects from the mirror. To the eye, the ray seems to come from behind the mirror. Because none of the rays actually emanate from the image, it is called a virtual image.

14. The geometry used to show that the image distance (di ) is equal • to the object distance (d0 ). • The two angles labeled θ are equal, (Law of Reflection). • The angle α is also equal to θ (opposite angles formed by intersecting lines). • β1 = β2 • Therefore, d0 = di

15. 25.3 The Formation of Images by a Plane Mirror Conceptual Example 1 Full-Length Versus Half-Length Mirrors What is the minimum mirror height necessary for her to see her full image?

16. 25.3 The Formation of Images by a Plane Mirror Conceptual Example 1 Full-Length Versus Half-Length Mirrors What is the minimum mirror height necessary for her to see her full image? Half her height.

17. Two plane mirrors form a right angle. How many images of the ball can you see in the mirrors? 1 2 3 4

18. Two plane mirrors form a right angle. How many images of the ball can you see in the mirrors? 1 2 3 4 There are 2 images from single reflections and and 2 images from double reflections

19. Law of Reflection Problem The tilted mirror in reflects a horizontal laser beam so that the reflected beam is 60˚ from horizontal. What is the angle ɸ?

20. Law of Reflection Problem The tilted mirror in reflects a horizontal laser beam so that the reflected beam is 60˚ from horizontal. What is the angle ɸ? ɸ = 30˚

21. 25.4 Spherical Mirrors • If the inside surface of the spherical mirror is polished, it is a concave • mirror. If the outside surface is polished, is it a convex mirror. • The law of reflection applies, just as it does for a plane mirror, with the normal (not shown above) drawn at the point where the incident light ray strikes the mirror. • The center of curvature, is located at point C, and the radius of curvature is R. • The principal axis of the mirror is a straight line drawn through the • center and the midpoint of the mirror.

22. 25.4 Spherical Mirrors – Concave Mirrors • A point on the tree lies on the principal axis of the concave mirror. • Rays from that point that are near the principal axis (paraxial rays) reflect and then cross the principal axis at the same place, at the image point. • Light rays diverge from the image point, just as they would from an actual object. • Since light rays actually come from the image point, this is a real image, and not a virtual image, as with the plane mirror.

23. 25.4 Spherical Mirrors – concave mirrors If the object is infinitely far from the mirror, the light rays become parallel to the principal axis as they get close to the mirror. In this special case, the image point is called the focal point, F. The focal length f is the distance between the focal point and the mirror.

24. 25.4 Spherical Mirrors It can be shown that the focal point of a concave mirror is halfway between the center of curvature of the mirror C and the mirror at B. Therefore the focal length, f, is one half the radius of curvature:

25. 25.4 Spherical Mirrors Rays that are far from the principal axis do not converge at the focal point. The fact that a spherical mirror does not bring all parallel rays to a single point is known as spherical abberation. We will consider only paraxial rays in our analysis.

26. 25.4 Spherical Mirrors When paraxial light rays that are parallel to the principal axis strike a convex mirror, the rays appear to originate from the focal point. The image is a virtual image.

27. 25.5 The Formation of Images by Spherical Mirrors RAY TRACING FOR CONCAVE MIRRORS – Use these 3 rays 1. This ray is initially parallel to the principal axis and passes through the focal point. 2. This ray initially passes through the focal point, then emerges parallel to the principal axis. 3. This ray travels along a line that passes through the center.

28. 25.5 The Formation of Images by Spherical Mirrors Image Formation – Concave Mirrors When the object (red arrow) is placed between the center of curvature and the focal point, the resulting image is real, enlarged, and inverted, relative to the object. In order to see a real image, you need to place a screen at the image point

29. 25.5 The Formation of Images by Spherical Mirrors Image Formation – Concave Mirrors When the object (red arrow) is located beyond the center of curvature, the resulting image is real, reduced, and inverted, relative to the object. In order to see a real image, you need to place a screen at the image point.

30. 25.5 The Formation of Images by Spherical Mirrors When an object is located between the focal point and a concave mirror, and enlarged, upright, and virtual image is produced.

31. Ray diagram applet www.phy.ntnu.edu.tw/java/Lens/lens_e.html

32. 25.5 The Formation of Images by Spherical Mirrors

33. 25.5 The Formation of Images by Spherical Mirrors CONVEX MIRRORS Ray 1 is initially parallel to the principal axis and appears to originate from the focal point. Ray 2 heads towards the focal point, emerging parallel to the principal axis. Ray 3 travels toward the center of curvature and reflects back on itself.

34. 25.5 The Formation of Images by Spherical Mirrors The virtual image is diminished in size and upright.

35. 25.6 The Mirror Equation and Magnification (Negative for convex lens) (Negative for virtual images) (Negative for inverted image)

36. 25.6 The Mirror Equation and Magnification Summary of Sign Conventions for Spherical Mirrors

37. 25.6 The Mirror Equation and Magnification These diagrams are used to derive the mirror equation.

38. 25.6 The Mirror Equation and Magnification Example 5 A Virtual Image Formed by a Convex Mirror A convex mirror is used to reflect light from an object placed 66 cm in front of the mirror. The focal length of the mirror is -46 cm. Find the location of the image and the magnification.

39. 25.6 The Mirror Equation and Magnification Example 5 A Virtual Image Formed by a Convex Mirror A convex mirror is used to reflect light from an object placed 66 cm in front of the mirror. The focal length of the mirror is -46 cm. Find the location of the image and the magnification.

40. Analyzing a concave mirror A 3.0 cm object is located 20 cm from a concave mirror. The radius of curvature is 80 cm. Determine the position, orientation and height of the image.

41. Analyzing a concave mirror A 3.0 cm-high object is located 20 cm from a concave mirror. The radius of curvature is 80 cm. Determine the position, orientation and height of the image. di = -40 cm, therefore image is virtual (behind mirror). m = +2.0, therefore object is upright and is 6.0 cm high.

42. A concave mirror of focal length f forms an image of the moon (very distant object). Where is the image located? • Almost exactly a distance f behind  the mirror. • Almost exactly a distance f in front  of the mirror. • At a distance behind the mirror equal to the distance of the moon in front of the mirror. • At the mirror’s surface.

43. A concave mirror of focal length f forms an image of the moon. Where is the image located? • Almost exactly a distance f behind  the mirror. • Almost exactly a distance f in front  of the mirror. • At a distance behind the mirror equal to the distance of the moon in  front of the mirror. • At the mirror’s surface.