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Geometrical Optics: Mirrors and Lenses Fundamentals

Dive into the principles of mirrors and lenses, understand image formation, mirror equations, and the thin lens concept. Quiz and exam preparation included. Practice with concave and convex mirror calculations. Learn the lensmaker's equation and graphical methods for optical systems analysis. Enhance your understanding of geometric optics in this comprehensive guide.

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Geometrical Optics: Mirrors and Lenses Fundamentals

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  1. Geometrical Optics – Part II Chapter 24

  2. Going Backwards

  3. Stuff • We continue with mirrors and lenses and even refractive surfaces. • Quiz on Friday • For a while, office hours will be in, of all places, my office. We really don’t need MAP-318 except before exams. And the hours are too confusing. • Next Exam is on Wednesday, December 2nd. • I give up on the remaining evil clickers. Clicker grade=0. • Let’s move on.

  4. R When the Center of Curvature is on the same side of the outgoing ray, R is positive. Otherwise, if the center of curvature is not on the same side as the outgoing ray, R is negative.

  5. Concave Mirror/Paraxial Approximation Consequently MIRROR EQUATION Mirror, mirror on the wall…

  6. Image Formation ‘ ‘ y’<0 (from the diagram) so image is inverted.

  7. The geometry……

  8. Let’s try an example

  9. A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 15 cm from the mirror. 10 cm 5 cm Normal to mirror and bounces back along incoming path.

  10. A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 10 cm from the mirror. 10 cm 5 cm

  11. A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 2.5 cm from the mirror. virtual image 10 cm 5 cm eye

  12. The Concave Mirror The Equations are the same as the convex mirror but the Radius of the mirror is negative

  13. More Convex Mirror

  14. Graphical Methods are very useful to check your work.

  15. Moving on to refractive surfaces

  16. Spherical Refractive Surfaces air glass

  17. A closer look atthe Math ….

  18. No for the height of the image

  19. Check this out – how big is R?

  20. From the math:

  21. The Thin Lens

  22. The Thin Lens • We ignore the thickness of the lens. • We will use mostly geometrical methods. • Any ray that bends is assumed to bend only once at the center of the lens.

  23. From whence it came Surface 2 Surface 1 n>1 n=1 n=1.5 n=1 Surface 2

  24. The thin lens - geometry parallel

  25. More Geometry • Lens is thin • Actual thickness of the lens is ignored. • Image from first surface provides the object for the second surface. • Paraxial Ray Approximation • sin(x)=tan(x)=x • cos(x)=1 • x is in RADIANS

  26. More Geometry Triangle PQO and triangle P’Q’O are similar. We willshow that for a very thin lens: F1=F2=f The Thin Lens Equation

  27. This, of course depends on where the object is placed with respect to f.

  28. Image that would form if material “a” was all on this side of the lens. Object for second surface. Thin Lens (con’t)

  29. Procedure for equation • Solve for image position for first surface • Use image as object for the second surface. • Use the refraction equation in both cases. For a lens. na=nc=1 So we can call the middle one just n Mess with the algebra and you will get:

  30. FINALLY – with some algebra and obvious substitutions, we get: The Lensmaker’s Equation Ta Daaa!

  31. Two Ways to do this STUFF • Algebraically using the lens equation (with the 1/f if you know it) • Using graphical Methods

  32. Graphical Methods:

  33. Graphical Methods:

  34. Most important case: converging lensObject to left of F1

  35. Most important case: converging lens

  36. Most important case: converging lens

  37. Most important case: converging lens

  38. Most important case: converging lens

  39. Most important case: converging lens So, now you know!

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