chapter36_thin%20lens%202

chapter36_thin%20lens%202 - Chapter 36 Image Formation 2 1...

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Chapter 36 Image Formation 2 1. Thin Lens 2. Multi lens/mirror system
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Spherical mirror formulas 1 1 1 p q f + = I O h q M h p = - Object distance, image distance and focal length: Focal length and sphere radius: 2 R f = Object distance, image distance and magnification: 2 R f = - Converging mirror Diverging mirror
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The lens maker’s formula (lens in vacuum or air) - - = 2 1 1 1 1 1 R R ) n ( f n : index of refraction of the lens material. R 1 : radius of near surface. R 2 : radius of far surface. The sign conventions for the radii of the two surfaces: 1. The near or far surface of the lens is with respect to the focal point F . Near side is surface 1, far side is surface 2. 2. The sign of the radius is then defined as: + ” if the center is on the far side; “ - ” if the center is on the near side 1. In this convention, positive f means converging lens, negative f means diverging lens. F near surface far surface
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More examples
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Steps to determine the signs circle6 Pick up the focal point, hence the focal length in question. circle6 Mark the near surface S 1 , and far surface S 2 . circle6 Based on the curve of these two surfaces, mark the center C 1 for S 1 and C 2 for S 2 . circle6 Mark R 1 for S 1 and R 2 for S 2 . circle6 Now decide on the sign of R 1 and R 2 , based on its center on far side (+) or near side (-).
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- - = 2 1 1 1 1 1 R R ) n n ( f medium lens F near surface far surface n medium The lens maker’s formula (lens in a medium)
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Example: prove for a thin lens, the focal length on both side of the lens is the same.
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