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Lecture 18 Ray Optics-4 Chapter 23

Lecture 18 Ray Optics-4 Chapter 23. PHYSICS 270 Dennis Papadopoulos March 24, 2010. Convex Mirror. Virtual Image – Rays Diverge. Tactics: Ray tracing for a spherical mirror. Tactics: Ray tracing for a spherical mirror. Optical axis. A parallel ray reflects through focal point

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Lecture 18 Ray Optics-4 Chapter 23

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  1. Lecture 18Ray Optics-4 Chapter 23 PHYSICS 270 Dennis Papadopoulos March 24, 2010

  2. Convex Mirror Virtual Image – Rays Diverge

  3. Tactics: Ray tracing for a spherical mirror

  4. Tactics: Ray tracing for a spherical mirror

  5. Optical axis • A parallel ray reflects through focal point • A ray through the focal point reflects parallel to the axis • A ray striking the mirror center reflects at an equal angle on the opposite side of the axis

  6. Tactics: Ray tracing for a spherical mirror

  7. A Little Math

  8. Take rays near axis, paraxial rays The excess time along OP vs. OQ is h2/2s and the excess time on the PO’ route vs. QO’ is n(h2/2s’). This is compensated by the delay time from V to Q (Notice that we took the VQ distance as traveled at c). This delay time is (n-1)VQ. For a spherical surface with radius R, VQ=h2/2R. We thus have See equ. 23.21 of the book with n1=1, n2=n

  9. Details of mathematical proof h These are the excess time along OP and along PO’ if we assume that the distance VQ is covered at speed at the vacuum speed c and not v. In other words the time to go from V to Q is not as it was straight in vacuum but slower by the factor v/c. So the excess delay is then Q For light to arrive at the same time travelling the path OVO’ and the path OPO’ we must have Where VQ= h2/2R

  10. A paraxial ray • moves in a parabolic path. • is a ray that has been reflected from parabolic mirror. • is a ray that moves nearly parallel to the optical axis. • is a ray that moves exactly parallel to the optical axis.

  11. A paraxial ray • moves in a parabolic path. • is a ray that has been reflected from parabolic mirror. • is a ray that moves nearly parallel to the optical axis. • is a ray that moves exactly parallel to the optical axis.

  12. The Mirror Equation For a spherical mirror with negligible thickness, the object and image distances are related by where the focal length f is related to the mirror’s radius of curvature by

  13. What is specular reflection? • The image of a specimen. • A reflection that separates different colors. • Reflection by a flat smooth object. • When the image is virtual and special.

  14. What is specular reflection? • The image of a specimen. • A reflection that separates different colors. • Reflection by a flat smooth object. • When the image is virtual and special.

  15. A virtual image is • the cause of optical illusions. • a point from which rays appear to diverge. • an image that only seems to exist. • the image that is left in space after you remove a viewing screen.

  16. A virtual image is • the cause of optical illusions. • a point from which rays appear to diverge. • an image that only seems to exist. • the image that is left in space after you remove a viewing screen.

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