Chapter 23. Ray Optics 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. In this chapter you will learn: • Use the ray model of light • Calculate angles of reflection and refraction • Understand the color and dispersion • Use ray tracing to analyze lens and mirror systems • Use refraction theory to calculate the properties of lens systerm

Reading assignment The Ray Model of Light Reflection Refraction Image Formation by Refraction Color and Dispersion Thin Lenses: Ray Tracing Thin Lenses: Refraction Theory Image Formation with Spherical Mirrors

Stop to think 23. 1. page 703 Stop to think 23. 2 Stop to think 23.1 page 703 Stop to think 23.2 page706 Stop to think 23.3 page 711 Stop to think 23.4 page 720 Stop to think 23.5 page 724 Stop to think 23.6 page 731 Example 23.2 page 705 Example 23.4 page 709 Example 23.9 page 719 Example 23.11 page 722 Example 23.17 page 730

Propagation of Light – Ray (Geometric) Optics Main assumption: light travels in a straight-line path in a uniform medium and changes its direction when it meets the surface of a different medium or if the optical properties of the medium are nonuniform The rays (directions of propagation) are straight lines perpendicular to the wave fronts The above assumption is valid only when the size of the barrier (or the size of the media) is much larger than the wavelength of light

Stop to think 23.1 A long, thin light bulb illuminates a vertical aperture. Which pattern of light do you see on a viewing screen behind the aperture?

Reading quiz 1

Reading quiz 2

Reflection The law of reflection states that The incident ray and the reflected ray are in the same plane normal to the surface, and The angle of reflection equals the angle of incidence: θr = θi

Reflection of Light Specular reflection (reflection from a smooth surface) – example: mirrors Diffuse reflection (reflection from a rough surface)

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. That is, s' = s.

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

Two plane mirrors form a right angle Two plane mirrors form a right angle. How many images of the ball can you see in the mirrors? 1 2 3 4 STT23.2

Refraction Snell’s law states that if a ray refracts between medium 1 and medium 2, having indices of refraction n1 an n2, the ray angles θ1 and θ2 in the two media are related by Notice that Snell’s law does not mention which is the incident angle and which is the refracted angle.

Refraction – Snell’s Law The incident ray, the refracted ray, and the normal all lie on the same plane The angle of refraction is related to the angle of incidence as v1 is the speed of the light in the first medium and v2 is its speed in the second Since and , we get , or Snell’s Law index of refraction

Refraction in a Prism Since all the colors have different angles of deviation, white light will spread out into a spectrum Violet deviates the most Red deviates the least The remaining colors are in between

EXAMPLE 23.4 Measuring the index of refraction

Total Internal Reflection

Fiber Optics Total Internal Reflection: Application ( ) Plastic or glass rods are used to “pipe” light from one place to another Applications include: medical use of fiber optic cables for diagnosis and correction of medical problems Telecommunications

A triangular glass prism with an apex angle of Ф=60o has an index of refraction n=1.5. What is the smallest angle of incidence for which a light ray can emerge from the other side?

Thin Lenses: Ray Tracing

Thin Lenses: Ray Tracing

Thin Lenses: Ray Tracing

Lateral Magnification The image can be either larger or smaller than the object, depending on the location and focal length of the lens. The lateral magnification m is defined as A positive value of m indicates that the image is upright relative to the object. A negative value of m indicates that the image is inverted relative to the object. The absolute value of m gives the size ratio of the image and object: h'/h = |m| .

Important Concepts

Applications

Applications

The Thin Lens Equation The object distance s is related to the image distance s' by where f is the focal length of the lens, which can be found from where R1 is the radius of curvature of the first surface, and R2 is the radius of curvature of the second surface, and the material surrounding the lens has n = 1.

Tactics: Ray tracing for a spherical mirror

The Mirror Equation For a spherical mirror with negligible thickness, the object and image distances are related by where the focal length f is related to the mirror’s radius of curvature by