chapter 23. ray optics our everyday experience that light travels in straight lines is the basis of...

Chapter 23. Ray OpticsChapter 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 assignmentReading 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 703Stop to think 23.2 page706Stop to think 23.3 page 711Stop to think 23.4 page 720Stop to think 23.5 page 724Stop to think 23.6 page 731

Example 23.2 page 705Example 23.4 page 709Example 23.9 page 719Example 23.11 page 722Example 23.17 page 730

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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

d

Stop to think 23.1A 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

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A virtual image is

A.the cause of optical illusions.B.a point from which rays appear

to diverge.C.an image that only seems to

exist.D.the image that is left in space

after you remove a viewing screen.

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A virtual image is

A.the cause of optical illusions.B.a point from which rays

appear to diverge.C.an image that only seems to

exist.D.the image that is left in space

after you remove a viewing screen.

Reading quiz 2

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The focal length of a converging lens is

A.the distance at which an image is formed.

B.the distance at which an object must be placed to form an image.

C.the distance at which parallel light rays are focused.

D.the distance from the front surface to the back surface.

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The focal length of a converging lens is

A.the distance at which an image is formed.

B.the distance at which an object must be placed to form an image.

C.the distance at which parallel light rays are focused.

D.the distance from the front surface to the back surface.

ReflectionThe law of reflection states that1. The incident ray and the reflected ray are in the

same plane normal to the surface, and2. The angle of reflection equals the angle of

incidence: θr = θi

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Reflection of Light

Diffuse reflection (reflection from a rough surface)

Specular reflection (reflection from a smooth surface) – example: mirrors

The Plane MirrorConsider 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?

A. 1

B. 2

C. 3

D. 4

A. 1

B. 2

C. 3

D. 4

Two plane mirrors form a right angle. How many images of the ball can you see in the mirrors?

RefractionSnell’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.

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• 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

Refraction – Snell’s Law

2 2

1 1

sin

sin

v

v

Since and , we get , or11

cv

n 2

2

cv

n

index of refraction

2 2 2 1

1 1 1 2

sin /

sin /

v c n n

v c n n

2 2 1 1sin sinn n

Snell’s Law

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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

1 2 '

min , 2 2 1 min

min1

2

when ' ,2 2

sin( )sin 2n=sin sin

2

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EXAMPLE 23.4 Measuring the index of refraction

QUESTION:

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EXAMPLE 23.4 Measuring the index of refraction

EXAMPLE 23.4 Measuring the index of refraction

Total Internal Reflection

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• 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

Total Internal Reflection: Application

Fiber OpticsTotal Internal Reflection( )incidence cr

A triangular glass prism with an apex angle of Ф=60o has anindex of refraction n=1.5. What is the smallest angle of incidence

for which a light ray can emerge from the other side?

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Color

Different colors are associated with light of different wavelengths. The longest wavelengths are perceived as red light and the shortest as violet light. Table 23.2 is a brief summary of the visible spectrum of light.

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Dispersion

The slight variation of index of refraction with wavelength is known as dispersion. Shown is the dispersion curves of two common glasses. Notice that nis larger when the wavelength is shorter, thus violet light refracts more than red light.

Thin Lenses: Ray Tracing

Thin Lenses: Ray Tracing

Thin Lenses: Ray Tracing

Lateral MagnificationThe 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

1. 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.

2. The absolute value of m gives the size ratio of the image and object: h'/h = |m| .

Important Concepts

Applications

Applications

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Thin Lenses: Refraction Theory

Consider a spherical boundary between two transparent media with indices of refraction n1 and n2. The sphere has radius of curvature R and is centered at point C.

The Thin Lens Equation

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.

The object distance s is related to the image distance s' by

Tactics: Ray tracing for a spherical mirror

The Mirror EquationFor 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