Ray Optics. Physics 11. Sources of Light Rays: Self-Luminous Objects. The Ray Model of Light

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1 Physics 11 Ray Optics Ray Model of Light Reflection Plane Mirrors Spherical Mirrors Ray Tracing Images from a Concave Mirror Images from a Convex Mirror Slide 18-3 The Ray Model of Light Sources of Light Rays: Self-Luminous Objects A ray source A point source Light rays travel in straight lines. Light rays can cross. A light ray travels forever unless it interacts with matter. An extended source A parallel-ray source An object is a source of light rays. The eye sees by focusing a bundle of rays. Slide 18-9 Slide

2 Wave Fronts and Rays Wave Fronts and Light Rays Wave fronts are surfaces that are in the same phase of motion. Rays are radial lines pointing outward from the source and perpendicular to the wave fronts. At large distances from the source, the wave fronts become flat surfaces known as plane waves. The Law of Reflection Law of Reflection 1. The incident ray and the reflected ray are both in the same plane, which is perpendicular to the surface, and 2. The angle of reflection equals the angle of incidence: θr = θi. Slide The incident ray, the reflected ray, and the normal to the surface all lie in the same plane. The angle of incidence equals the angle of reflection: i r 2

3 Specular Reflection Diffuse Reflection Seeing Objects Seeing a point or extended source Seeing an object by scattered light Plane Mirror Seeing a ray source Slide The image from a plane mirror is upright, the same size as the object, and as far behind the mirror as the object is in front of it. 3

4 The Plane Mirror Plane Mirror The image from a plane mirror is virtual. Slide Plane Mirror Plane Mirror To view one s full length in a mirror, only a half-length mirror is needed. 4

5 Spherical Mirrors Concave and Convex Mirrors Concave Mirror Convex Mirror A spherical mirror has the shape of a section from the surface of a sphere. Image Point Focal Point f = ½ R Light rays from a source cross at a common point (called the image point) after reflection from a concave mirror. If the light rays are parallel to the principal axis, they cross at a special point called the focal point F. The distance from the center of the mirror to the focal point is called the focal length f. 5

6 Spherical Aberration Convex Mirror f = - ½ R Only light rays close to the principal axis (paraxial rays) cross the focal point. For a convex mirror, parallel paraxial rays appear to originate from the focal point F. Spherical Mirrors and Ray Tracing A Real Image Formed by a Concave Mirror The focal point of a concave mirror The focal point of a convex mirror Slide Slide

7 Three Sets of Special Rays for a Concave Mirror Ray Tracing Ray 1: A ray initially parallel to the principle axis will be reflected through the focal point. Slide Ray Tracing Ray Tracing Ray 2: A ray passing through the focal point will be reflected parallel to the principal axis. Ray 3: A ray that travels along a line that passes through the center of curvature C be be reflected upon itself. 7

8 Images from a Concave Mirror Images from a Concave Mirror A object placed between C and F will produce a real, enlarged, inverted image beyond the center of curvature C. A object placed beyond C will produce a real, reduced, inverted image between C and F. Images from a Concave Mirror A object placed between F and the mirror will produce a virtual, enlarged, upright image. Slide

9 Ray Tracing for a Convex Mirror Three Sets of Special Rays for a Convex Mirror Slide Slide Images from a Convex Mirror The image produced by a convex mirror is always virtual, reduced, and upright. Slide

10 Refraction of Light Refraction of Light Refraction: The bending of light when it passes from one transparent material to another. When light passes from a material with a lower index of refraction to a material with a higher index of refraction (n 1 < n 2 ), it is bent toward the normal. Refraction of Light Refraction of Light To understand why light bends when passing from one transparent material to another, imagine a cartwheel rolling from a sidewalk onto grass. When light passes from a material with a higher index of refraction to a material with a lower index of refraction (n 2 > n 1 ), it is bent away from the normal. Because the wheels roll slower in the grass, the left wheel will slow down first causing the cartwheel to change directions. 10

11 Refraction of Light Similarly, when light hits a transparent material like water where the speed of light is slower, one side of the wavefront slows down before the other side. Because light travels slower in the water, the left side of the wavefront will slow down first, causing the light to bend. Total Internal Reflection As the angle of incidence is increased, the angle of refraction increases until eventually it equals 90 o. The angle of incidence at which this happens is known as the critical angle c. Total Internal Reflection Total Internal Reflection When light tries to go from one transparent material into another transparent material where the speed of light is greater, the light will get totally internally reflected (no light gets refracted out) if the angle the light hits at is greater than a certain angle called the critical angle. If the angle of incidence is greater than the critical angle c, no refraction takes place and the light is totally internally reflected. 11

12 Total Internal Reflection Total Internal Reflection Diamonds sparkle because of total internal reflection Total Internal Reflection Total Internal Reflection 12

13 Thin Lenses Thin Lenses If n lens > n surrounding medium : Lenses thicker in the middle than at the edges are converging. Lenses thinner in the middle than at the edges are diverging. Ray Tracing: Converging Lens Ray Tracing: Converging Lens Ray 1: a ray initially parallel to the central axis is refracted through the focal point on the right side of the lens. Ray 2: a ray through focal point on the left side of the lens is refracted parallel to the central axis. 13

14 Ray Tracing: Converging Lens Converging Lens Ray 3: a ray directly through the center of the lens is not refracted. An object between F and the lens will create a virtual, upright, and enlarged image. Converging Lens Converging Lens An object between F and 2F will create a real, inverted, and enlarged image. An object beyond 2F will create a real, inverted, and reduced image. 14

15 Ray Tracing: Diverging Lens Ray Tracing: Diverging Lens Ray 1: a ray initially parallel to the central axis appears to have originated from the focal point on the left side of the lens Ray 2: a ray traveling towards the focal point on the right side of the lens is refracted parallel to the principle axis Ray Tracing: Diverging Lens Diverging Lens Ray 3: a ray directly through the center of the lens is not refracted A diverging lens always creates a virtual, upright, and reduced image. 15

16 Lenses in Combination When lenses are used in combination, the image from the first lens becomes the object for the second lens. 16