Physics 123C Waves

1. Physics 123C Waves Lecture 9Ray Optics

2. Models of Light Is light a particle or a wave? Physics in the 20th century has shown that this simple question does not have a simple answer. The behavior of light, depending on the circumstances, can be described by three distinct (and seemingly contradictory) models. We will introduce all of them and learn the conditions and circumstances under which each is valid. The Wave Model: This model works in many circumstances. When it is applicable, light shows the same interference behavior as water waves and sound waves. Lasers and electro-optical devices, critical technologies of the 21st century, are best understood with the wave model of light, which we will call wave optics. The Photon Model: This model works in circumstances where energy detection is important, as describes light as a stream of photons, particles that carry packets of energy called quanta. The Ray Model: Light travels in straight lines, modified by reflection and refraction. This model works best for optical instruments and lenses, and is the basis for ray optics.

3. The Ray Model of Light Light travels in straight lines. Light rays can cross. They do not interact. Light rays travel forever unless they interact with matter. Matter can reflect, refract, and absorb light. An illuminated object is a source of light rays. The eye sees by focusing a diverging bundle of light rays to an image.

4. Objects A source of light can be either self-luminous (e.g., the Sun or a light bulb) or reflective (e.g., the page of a book or a projection screen). Most objects are reflective. Light rays exist everywhere, independent of whether you see them or not. We will often idealize groups by describing them as rays from a point source or in a parallel bundle. A light from a laser or from a distant object can be considered a parallel bundle.

5. Ray Diagrams We will often simplify the situation in ray optics by drawing a ray diagram, in which we consider only the light emitted from a few representative points. For example, we consider rays from the top and bottom of a tree rather than from the whole tree.

6. A Pinhole “Camera” In Roman and medieval times, the camera obscura (literally “darkened chamber”) was a popular form of entertainment. Participants would enter a darkened room with a pinhole admitting light at one end. When their eyes adapted, they would see full color images of the outside world on the opposite wall, but with everything turned upside down. Ray tracing explains this device. The pinhole admits only selected rays, and these trace the image on the wall. By similar triangles, the image height is hi = hodi/do. Thus, the magnification is m = hi/ho = di/do. The smaller the pinhole (ignoring diffraction), the sharper (and dimmer) is the image.

7. Apertures A hole or restriction through which light passes is called an aperture. It selects the rays that are allowed to pass from light source to screen. A point source and extended aperture create an upright image of the aperture on the screen. An extended source and point aperture create an inverted image of the source on the screen.

8. Clicker Question 1 A long thin fluorescent tube illuminates a vertical slit aperture. Which pattern would you see on the screen behind the aperture?

9. Reflection Reflection from a flat smooth surface is called specular reflection (from speculum, Latin for mirror). The figure shows a bundle of parallel rays striking a reflective surface. The plane of the bundle is perpendicular to the reflective surface, and the reflected rays lie in the bundle plane. A better way of representing the situation is to draw the plane formed by the incident and reflected rays. Here: • The incident and reflected rays are in the same plane, which is normal to the reflecting surface. • The angle of incidence qi, (as measured from the normal) is equal to the angle of reflection qr.

10. Example:Light Reflecting from a Mirror A dressing mirror on a closet door is 1.5 m tall. The bottom is 0.5 m above the floor. A bare light bulb hangs 1.0 m from the closet door and 2.5 m above the floor. How long is the streak of light reflected across the floor?

11. Diffuse Reflection The reflection from an irregular surface obeys the law of reflection at any point, but the net effect is to reflect rays in many random directions, so that each small region becomes effectively a point source of reflected light.

12. Analysis of a Plane Mirror • Any point P on an object acts as a point source of light, producing many rays that are reflected by the mirror in different directions. • The reflection of each incident ray can be constructed using the law of reflection. • The reflected rays can be extrapolated backward to the point P’ from which they seem to emanate. Point P’ is the virtual image of point P, when viewed by reflection. This construction shows that the object distance s and the image distance s’ are equal.

13. Mirror Images • Rays from the extended object spread out and strike every point on the mirror surface. However, only a few of these rays reach your eye. • Rays from points P and Q enter your eye after reflection from different regions of the mirror surface. If the lower part of the mirror were removed, point Q would not be visible.

14. Left/Right Reflection Paradox: Why does a mirror reverse left and right when it does not reverse up and down? Answer: A mirror reverses neither left and right nor up and down. It reverses front and back. This has the effect of making a left hand into a right hand, and vice versa.

15. Curved Mirrors If a mirror is part of a spherical surface, parallel rays at different distances from the center line will converge in different places. This is called spherical aberration. However, if the mirror is only a small part of the spherical surface (so that the small-angle approximation is valid), parallel rays will focus at a distance that is ½ the mirror’s radius of curvature r. This is called the focal point f.

16. 3 3 Ray Tracing For spherical mirrors, one can geometrically construct the image point by using “special” rays: • A ray from the object that is parallel to the principal axis will be reflected through the focal point; • A ray from the object through the focal point will be reflected parallel to the principal axis; • A ray from the object along a radius will be reflected back along the radius; • A ray (dashed) to the mirror center (A) will be reflected at an equal and opposite angle; • The image is at the cross point.

17. Object Outside the Focus When the object is farther from the mirror than the focal point f, a real inverted image is formed. Here “real” means that rays actually pass through the image point I’ and “inverted” means that the image is upside-down with respect to the object.

18. Object Inside the Focus When the object is closer to the mirror than the focal point f, a virtual upright image is formed. Here “virtual” means that rays do not pass through the image point I’ and “upright” means that the image has the same up/down orientation as the object. This gives the magnifying effect of a shaving mirror.

19. q L q I C O g b a 0 r di do Mirror Equation Derivation

20. The Mirror Equations

21. Convex Mirrors Convex mirrors have a virtual focus, in that reflected parallel rays diverge, but can be extrapolated backwards to the focal point F. The image of an object in front of a convex mirror is always virtual upright with a magnification less than 1.

22. Five Things You Should Have Learned from This Lecture • The ray model of light assumes that light travels as a ray in a straight line unless reflected or refracted. • Apertures restrict light rays from an object, and can be used to form “pinhole camera” images. • A plane mirror reflects light so that the angle of incidence and the angle of reflection are equal. A plane mirror forms an image that is the same distance behind the mirror as the object is in front. • A spherical mirror can bring parallel rays to a focus and form images of objects. Ray tracing with “special rays” can be used to geometrically construct image positions and sizes. • A convex mirror has a virtual focal point and produces virtual upright images with magnification less than 1.