By R. Bronson

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Extra info for Differential Equations Crash Course

Example text

26 1. GEOMETRICAL OPTICS Calculation of Graph for xi as Function of xo over the Total Range of xo Graph for xi as function of xo over the range of xo to the left of f . Graph for xi as function of xo over the range of xo to the right of f . 031 . . 100 1 xi(xo) : . 031 . . − 11 1 xxi(xxo) : . 6. 031 . . 50 1 . 10. 1. Observe the singularity at the object focus, which has the same absolute value as the focal length but with a negative sign. The image focus has a positive sign. Note that they play different roles in the geometrical construction of the image.

We find the top of an image arrow at the image position, at −30. We call the image, obtained by tracing the diverging rays back to a converging point, a virtual image. A virtual image may serve as a real object for a second imaging process. 1 the image positions for real object positions discussed so far and have indicated for images and objects if they are real or virtual. 4. 6 (a) The C-ray and the PF-ray diverge in the forward direction; (b) they are traced back to the virtual image. 5). 39) yi /yo .

Galilean telescope. 9 cm. If xo1 is large and the distance a between the two lenses is 20 cm, calculate xi2 , the image distance with respect to the negative lens. Calculate the magnification and show that for the object at infinity, one again has M −f1 /f2 . The distance between the two lenses is then f1 + f2 . Laser beam expander. A laser beam of diameter of 2 mm should be expanded to a beam of 20 mm. a. A biconvex and a biconcave lens should be used. The beam first passes the biconcave lens of focal length −5 mm.