Design a plano-convex lens made from BK7 glass to have a 100 mm focal length at

Question

Design a plano-convex lens made from BK7 glass to have a 100 mm focal length at 488 nm wavelength of blue light (Ar-ion laser, n = 1.52283). To test your design and to estimate the effective focal length of this thin lens (physical thickness of a lens is very small) consider a ray traveling parallel to the optical axis of the lens as shown in the figure below. Using full form of Snell’s law (without paraxial approximation, i.e. n1sin(a1) = n2sin(a2)), determine where the ray crosses the optical axis (after passing through the lens) for input rays 1 mm and 15 mm above the optical axis. Test the same lens (as designed for 488 nm light) also for rays of red light (1 mm and 15 mm above the optical axis) with wavelength of 632.8 nm (He-Ne laser, n = 1.51509). In all cases estimate your focal length from the spot where a convex surface of the lens intersects with the optical axis (see figure below). How can you explain your results a) for rays of the same color and b) for rays of different colors that enter the lens at the same height?

Explanation / Answer

1/f = (1.52283 - 1)* 1/R

R = 0.52283 f = 52.283 mm

tan(theta i) = 1/52.283

theta i = 1.1 degree

by Snells law is

1 sin 1.1 = 1.52283 * sin(theta)

theta = 0.722 degree

X' = 1/sin(0.722)

= 79.3246 mm

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