James T. Shipman Jerry D. Wilson Charles 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: θ I = θ R

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 Section 7.2

Sec 7.2 Refraction and Dispersion Refraction in the ray and wave approaches: θ 1 is the angle of incidence θ 2 is the angle of refraction If η air ≤ η Glass ; θ 1 ≥ θ 2 If η air ≥ η Glass ; θ 1 ≤ θ 2

Sec 7.2 Refraction and Dispersion From air into water, if θ 1 ≤ some critical angle, θ C, 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) C med 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