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Chapter 23. Ray Optics

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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

- 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 23.1page 703Stop to think 23.2page706Stop to think 23.3page 711Stop to think 23.4page 720Stop to think 23.5page 724Stop to think 23.6page 731

Example 23.2page 705

Example 23.4page 709

Example 23.9page 719

Example 23.11page 722

Example 23.17page 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?

C

- 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)

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. How many images of the ball can you see in the mirrors?

1

2

3

4

C

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

Total Internal Reflection: Application

Fiber Optics

Total Internal Reflection

( )

- 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 anindex of refraction n=1.5. What is the smallest angle of incidencefor which a light ray can emerge from the other side?

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| .