Reflection and Refraction Chapter 26 Reflection and Refraction

A Brief History of Light 1000 AD It was proposed that light consisted of tiny particles Newton Used this particle model to explain reflection and refraction Huygens 1670 Explained many properties of light by proposing light was wave-like

A Brief History of Light, cont Young 1801 Strong support for wave theory by showing interference Maxwell 1865 Electromagnetic waves travel at the speed of light

A Brief History of Light, final Planck EM radiation is quantized Implies particles Explained light spectrum emitted by hot objects Einstein Particle nature of light Explained the photoelectric effect

Geometric Optics – Using a Ray Approximation Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different media 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

Ray Approximation A wave front is a surface passing through points of a wave that have the same phase and amplitude The rays, corresponding to the direction of the wave motion, are perpendicular to the wave fronts

Reflection of Light A ray of light, the incident ray, travels in a medium When it encounters a boundary with a second medium, part of the incident ray is reflected back into the first medium This means it is directed backward into the first medium

Specular Reflection Specular reflection is reflection from a smooth surface The reflected rays are parallel to each other All reflection in this text is assumed to be specular

Diffuse Reflection Diffuse reflection is reflection from a rough surface The reflected rays travel in a variety of directions Diffuse reflection makes the road easy to see at night

Law of Reflection The normal is a line perpendicular to the surface It is at the point where the incident ray strikes the surface The incident ray makes an angle of θ1 with the normal The reflected ray makes an angle of θ1’ with the normal

Law of Reflection, cont The angle of reflection is equal to the angle of incidence θ1= θ1’

Image forms at the point where the light rays converge. When we talk about an image, start from an ideal point light source. Every object can be constructed as a collection of point light sources. VIRTUAL IMAGE |q| p Image forms at the point where the light rays converge. When real light rays converge  Real Image When imaginary extension of L.R. converge  Virtual Image Only real image can be viewed on screen placed at the spot.

For plane mirror: p = |q| IMAGE VIRTUAL For plane mirror: p = |q| How about left-right? Let’s check?

Parallel light rays: your point light source is very far away. Spherical Mirror R: radius of curvature focal Point f: focal length = R/2 Optical axis concave convex Parallel light rays: your point light source is very far away. Focal point: (i) Parallel incident rays converge after reflection (ii) image of a far away point light source forms (iii) On the optical axis

Spherical Aberration Reflected rays do not converge: Not well-defined focal point not clear image Spherical Aberration f = R/2 holds strictly for a very narrow beam. Parabolic mirror can fix this problem.

Spherical Aberration: some mirrors were ground wrong by 1/50th of human hair thickness.

Notation for Mirrors The object distance is the distance from the object to the mirror Denoted by p The image distance is the distance from the image to the mirror Denoted by q The lateral magnification of the mirror is the ratio of the image height to the object height Denoted by M

Types of Images for Mirrors A real image is one in which light actually passes through the image point Real images can be displayed on screens A virtual image is one in which the light does not pass through the image point The light appears to diverge from that point Virtual images cannot be displayed on screens

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

Flat Mirror Simplest possible mirror Properties of the image can be determined by geometry One ray starts at P, follows path PQ and reflects back on itself A second ray follows path PR and reflects according to the Law of Reflection

Properties of the Image Formed by a Flat Mirror The image is as far behind the mirror as the object is in front |q| = p The image is unmagnified The image height is the same as the object height h’ = h and M = 1 The image is virtual The image is upright It has the same orientation as the object There is an apparent left-right reversal in the image

Case 1: p > R p f q P > q Real Image

Case 2: p = R p = q Real Image

Case 3: f < p < R p < q Real Image

Case 4: p = f q = infinite

Case 5: p < f q < 0 Virtual Image

For a small object, f = R/2 (spherical mirror) Mirror Equation 1/p + 1/q = 1/f For a small object, f = R/2 (spherical mirror) 1/p + 1/q = 2/R Alert!! Be careful with the sign!! Negative means that it is inside the mirror!! p can never be negative (why?) negative q means the image is formed inside the mirror VIRTUAL How about f?

Focal point inside the mirror For a concave mirror: f > 0 Focal point inside the mirror f < 0 1/p + 1/q = 1/f < 0 : q should be negative.

All images formed by a convex mirror are VIRTUAL. 1/p + 1/q = 1/f < 0 : q should be negative. All images formed by a convex mirror are VIRTUAL. Magnification, M = -q/p Negative M means that the image is upside-down. For real images, q > 0 and M < 0 (upside-down).

Sign Conventions for Mirrors Quantity Positive When Negative When Object location (p) Object is in front of the mirror Object is behind the mirror Image location (q) Image is in front of mirror Image is behind mirror Image height (h’) Image is upright Image is inverted Focal length (f) and radius (R) Mirror is concave Mirror is convex Magnification (M)

Ex. 26.1 An object is placed at the center of curvature of a Mirror. Where is the image formed? Describe the image? 1/p + 1/q = 1/f f = R/2 Object is at the center: p = R 1/q = 1/f – 1/p = 2/R – 1/R = 1/R q = R > 0 (Real Image) M = -q/p = -R/R = -1 No magnification but upside-down

Up-right or Upside-down Ex. 26.2 A concave mirror has a 30 cm radius of curvature. If an object is placed 10 cm from the mirror, where will the image be found? f = R/2 = 15 cm, p = 10 cm 1/p + 1/q = 1/f  1/10 + 1/q = 1/15 3/30 + 1/q = 2/30 1/q = -1/30 q = -30 cm Case 5: p < f Real or Virtual Magnified or Reduced Up-right or Upside-down q < 0 M = -q/p = 3

Q. An upright image that is one-half as large as an object is needed to be formed on a screen in a laboratory experiment using only a concave mirror with 1 m radius of curvature. If you can make this image, I will give you $10. If you can’t you should pay me $10. Deal or no deal? Why? 1/p + 1/q = 1/f = 2/R > 0 M = -q/p = ½ > 0 should be a real image: q > 0 M = -q/p cannot be positive, if q > 0. No deal!!!