Lecture Objectives After this class you will be

Lecture Objectives After this class you will be able to: 1. Apply the Law of Reflection 2. Locate and state the properties of an image 3. Determine the focus of a concave mirror, given its radius of curvature 4. Make ray diagrams for a concave mirror to locate an image and state its properties. 5. Use the mirror equation with correct rules for signs. 6. Calculate Image Magnification 7. Do the #3 -6 for a convex mirror. 0. Polarization

Polarization of Light Waves • Each atom produces a wave with its own orientation of • All directions of the electric field vector are equally possible. • This is an unpolarized wave. • Natural Light is unpolarized. Central dot represents light travelling out of the plane

Linear Polarization • An unpolarized beam can be polarized by – Selective absorption – Scattering – Reflection Unpolarized Polarized

Polarization by Selective Absorption

θ I = I 0 cos 2θ Intensity after polaroid Intensity before polaroid For unpolarized light, a polaroid sheet reduces its intensity to half (sunglasses).

Polarization by Selective Absorption Io I I = Io cos 2 θ What happens at ө = 90◦?

A Sequence of Polarizers

Polaroids: Selective Absorption • E. H. Land discovered a material that polarizes light through selective absorption. – He called the material Polaroid. – The molecules readily absorb light whose electric field vector is parallel to their lengths and transmit light whose electric field vector is perpendicular to their lengths.

Polarization by Scattering • Horizontally and vertically polarized waves are emitted.

Polarization by Reflection • When an unpolarized light beam is reflected from a surface, the reflected light is – Completely polarized – Partially polarized – Unpolarized • It depends on the angle of incidence. – For one particular angle, the beam is completely polarized.

Dual Nature of Light • Light has a number of physical properties, some associated with waves and others with particles. • In considering reflection we will consider the light as a wave.

Reflection and Refraction When light traveling in one medium encounters a boundary leading to a second medium: • reflection, part of the light bounces off the second medium. • refraction, the light passing into the second medium bends. • Often, both processes occur at the same time.

Following the Reflected and Refracted Rays • Which rays are reflected rays and which are refracted?

Following the Reflected and Refracted Rays • Ray is the incident ray. • Ray is the reflected ray. • Ray is refracted into the Lucite. • Ray is internally reflected in the Lucite. • Ray is refracted as it enters the air from the Lucite.

Geometric Optics – Using a Ray Approximation • The ray approximation is used to represent beams of light. • A ray of light is an imaginary line drawn along the direction of travel of the light beams.

Diffuse Reflection • Diffuse reflection is reflection from a rough surface. • The reflected rays travel in a variety of directions.

Specular Reflection • Specular reflection is reflection from a smooth surface e. g. a mirror

1. Law of Reflection θ i= θ r

2. Plane Mirror Properties of the image can be determined by geometry.

Notation for Mirrors and Lenses • The object distance (p) is the distance from the object to the mirror or lens. • The image distance (q) is the distance from the image to the mirror or lens. – Images are formed at the point where rays actually intersect or appear to originate. • The lateral magnification (M) of the mirror or lens is the ratio of the image height to the object height.

Types of Images • Real images are formed at the point the rays of light actually intersect. • Virtual images are formed at the point the rays of light appear to originate. – The light appears to diverge from that point. – Virtual images cannot be displayed on screens.

3. Spherical Mirrors • A spherical mirror has the shape of a segment of a sphere. • A concave spherical mirror has the silvered surface of the mirror on the inner, or concave, side of the curve. • A convex spherical mirror has the silvered surface of the mirror on the outer, or convex, side of the curve.

Concave Mirror, Notation • The mirror has a radius of curvature of R. • Its center of curvature is the point C. • Point V is the center of the spherical segment. • A line drawn from C to V is called the principal axis of the mirror. • The focus is at half the distance of C

4. Ray Diagrams • A ray diagram can be used to determine the position and size of an image. • They are graphical constructions which tell the overall nature of the image. • They can also be used to check the parameters calculated from the mirror and magnification equations.

The Rays in a Ray Diagram • Ray 1 is drawn parallel to the principle axis and is reflected back through the focal point, f. Credit: Nerd Island Studios

The Rays in a Ray Diagram • Ray 2 is drawn through the center of curvature and is reflected back on itself.

The Rays in a Ray Diagram • Ray 3 is drawn through the focal point and is reflected parallel to the principal axis.

More About Images • To find where an image is formed, it is always necessary to follow at least two rays of light as they reflect from the mirror.

Ray Diagram for Concave Mirror, p > 2 f, Image is real, inverted and smaller. • The image is real, inverted and smaller than the object.

Ray Diagram for Concave Mirror, 2 f > p > f, Image is real, inverted and larger. • The image is real, inverted and larger than the object.

Ray Diagram for a Concave Mirror, p < f, Image is virtual, upright and enlarged • The image is virtual, upright and larger than the object.

Notes About the Rays • The rays actually go in all directions from the object. • The three rays were chosen for their ease of construction. • The image point obtained by the ray diagram must agree with the value of q calculated from the mirror equation.

Example 26. 1 An object is placed at the center of curvature of a concave mirror. Where is the image formed? Describe the image. Simulation

Example 26. 1 Solution Image properties: • Real • Inverted • Same size.