James T. ShipmanJerry D. WilsonCharles A. Higgins, Jr.

Optics and Wave Effects

Chapter 7

Sec 7.1 Reflection

Three approaches to the Study of Waves and Their effects:

• The Wave Approach: Waves have “wave fronts”- successive crests or troughs traveling away from a source• Plane Waves: Wave fronts are parallel planes, one

wavelength apart, with a source at infinity• Spherical Waves: Wave fronts are concentric circles in 2D

(spheres in 3D), one wavelength apart, with a source at their centers

• The Ray Approach: Waves are represented by arrows, that show only the direction of their propagation

Sec 7.1 Reflection

Three approaches to the Study of Waves and Their effects: • The Particle Approach: Waves are as a beam

of “particles” striking an object

Sec 7.1 Reflection

More Aspects of Wave Behavior• Reflection: The change in direction of a wave

when it strikes and rebounds from a surface or the boundary between two media• Reflection can be thought of as light “bouncing off” a

surface (although this phenomena is much more complex). Two types: • Regular (specular) reflection – reflection from very smooth

(mirror) surfaces• Irregular (diffuse) reflection – reflection from relatively rough

surfaces

Section 7.1

Sec 7.1 Reflection

• In reflection, the speed of the incident ray is the same as that of the reflected ray. • The Law of

Reflection: θI = θR

Sec 7.1 Reflection

• The law is obeyed in both types of reflection

Sec 7.1 Reflection

• A ray diagram is used to determine the apparent location of an image formed by a plane mirror.

Section 7.1

Sec 7.2 Refraction and Dispersion

• Refraction - bending of light waves caused by a speed change as light goes from one medium to another (the deviation of light from its original path because of a speed change)• Index of Refraction – ratio of the speed of light in a

vacuum to the speed of light in a medium

Section 7.2

Sec 7.2 Refraction and Dispersion

• Refraction in the ray and wave approaches: • θ1 is the angle of

incidence• θ2 is the angle of

refraction• If ηair ≤ ηGlass ; θ1 ≥ θ2 • If ηair ≥ ηGlass ; θ1 ≤ θ2

Sec 7.2 Refraction and Dispersion

• From air into water, if θ1 ≤ some critical angle, θC, then the ray is totally internally reflected

Sec 7.2 Refraction and Dispersion

• Mirages are real, not illusions

Sec 7.2 Refraction and Dispersion

Dispersion: White light is separated into component colors (wavelengths)• Cmed and η are slightly

wavelength dependent

• This is involved with prisms.

Sec 7.3 Spherical Mirrors

• Spherical mirror – a section of a sphere of radius R and with a center of curvature C

• The geometry of a spherical mirror can be described using several terms

• The radius (R) and center of curvature (C) of the entire sphere

• Principal axis – a line drawn through C to the mirror surface

• Vertex (V) – point where the principal axis intersects the mirror surface

• The focal point (F) and focal length (f)

Section 7.3

Sec 7.3 Spherical Mirrors

Concave (converging) Convex (diverging)

Sec 7.3 Spherical Mirrors

• Mirrors form images by reflection• Types of images:

• Virtual: When only one mirror is used, these are upright

• Real: When only one mirror is used, these are inverted• Real images can be formed on a screen• Virtual images cannot be formed on a screen

• Magnified: enlarged• Reduced: smaller

Sec 7.3 Spherical Mirrors

• Converging mirror: object between F and C• Image is upright (virtual)

and reduced

• Converging mirror object outside the center of curvature• Image is inverted (real)

and reduced

Sec 7.3 Spherical Mirrors

• Converging mirror: object closer than the focal point• Image is upright

(virtual) and reduced

Sec 7.3 Spherical Mirrors

• Diverging mirror• Object is upright

(virtual) and magnified

Sec 7.4 Lenses

• Lens – consists of material (plastic, glass) that refracts light waves to give an image of an object

• There are two main classes of lenses:– Converging or Convex lens – thicker at the center

than the edge– Diverging or Concave lens – thicker at the edges

Section 7.4

Sec 7.4 Lenses

• Lenses form images by refraction• Types of images:

• Virtual: When only one mirror is used, these are upright

• Real: When only one mirror is used, these are inverted• Real images can be formed on a screen• Virtual images cannot be formed on a screen

• Magnified: enlarged• Reduced: smaller

Sec 7.4 Lenses

Section 7.4

Sec 7.4 Lenses

Section 7.4

Sec 7.4 Lenses

• Converging lens: object inside of F• Image is virtual (upright)

and magnified

• Converging lens: object outside of F• Image is real (inverted)

Sec 7.4 Lenses

• Diverging lens: • Image is virtual and reduced

Sec 7.4 Lenses

• The human eye • We see because the

lens of the eye focuses a real (inverted) image on the retina• The brain turns the

image right-side-up. • The cilliary muscles

adjust the focal length such that the image is formed on the retina

Sec 7.4 Lenses

• Near point – the position closest to the eye at which objects can be seen clearly

• A person’s near point changes with age.– Children can usually focus on objects as close as 10

cm.– Young adults can usually focus on objects as close

as 12 to 15 cm.– Adults past 40 start having trouble focusing on

objects any closer than 25 cm.• As a person grows older their lens becomes less

deformable and therefore cannot focus as readily.

Section 7.4

Sec 7.5 Polarization

• Recall that light waves are transverse electromagnetic waves with both electric and magnetic field vectors. We are concerned with the electric vectors here.

Section 7.5

Sec 7.5 Polarization

• Any wave that is constrained to oscillate in a certain direction or along any plane, is said to be polarized in that plane.

Section 7.5

Sec 7.5 Polarization

• Polarization - the preferential orientation of the field vectors

• Polarization of light may be attained by several means, one of the most common is by the use of a polarizing (Polaroid) film.

• This type of polarizer only allows the component waves in a specific plane to pass.

• The human eye cannot detect whether light is polarized or unpolarized.

Section 7.5

Sec 7.5 Polarization

Section 7.5

Sec 7.5 Polarization

• Light passes through the first polarizer but will not pass through the second polarizer that is at a right angle to the first.

Section 7.5

Sec 7.6 Diffraction and Interference

• The bending of waves when moving past an opening or obstacle that has a size smaller than or equal to the wavelength.• Waves have the ability to move around an obstacle

• All waves – sound, light, water, etc. – show this type of bending as they go through relatively small slits or pass by the corners of objects.

• In general the larger the wavelength compared to the size of the opening or object, the greater the diffraction.

Section 7.6

Sec 7.6 Diffraction and Interference

Interference• When two or more waves meet, they pass right

through each other. As they do, they are said to “interfere” with each other.• Constructive: When the two waves tend to enhance

each other• Destructive: When the two wave tend to destroy each

other• The resulting waveform is a combination of the

individual waves. • Interference and Diffraction

Section 7.6