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Chapter 26

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.

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Chapter 26

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  1. Chapter 26 Reflection and Refraction

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

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

  12. |q| 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 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.

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

  14. focal Point f: focal length = R/2 Spherical Mirror R: radius of curvature 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

  15. 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.

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

  17. 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

  18. 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 virtualimage 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

  19. 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

  20. 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

  21. 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

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

  23. Case 2: p = R p = q Real Image

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

  25. Case 4: p = f q = infinite

  26. Case 5: p < f q <0 Virtual Image

  27. 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?

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

  29. 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).

  30. Sign Conventions for Mirrors

  31. 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

  32. 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? Case 5: p < f 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 q < 0 Real or Virtual Magnified or Reduced Up-right or Upside-down M = -q/p = 3

  33. 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!!!

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