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Understanding Light: Reflection, Refraction, and Optics in History

Explore the journey of light from particles to waves, reflection laws, types of images formed by mirrors, and geometric optics applications in a concise manner. Discover the significance of specular and diffuse reflection, virtual vs real images, and how to determine image properties using the mirror equation.

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Understanding Light: Reflection, Refraction, and Optics in History

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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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