I am looking for an expression to find out the magnification of a ball lens, for a given diameter of the lens. Literature review suggests that a 1 mm ball lens can provide 350X magnification, magnification of a ball lens decreases with increasing diameter. However, I have not been able to find out a proper expression by which the magnification of the ball lens can be defined. Can somebody help me to solve this?
Dear Rubdra, The effective focal length of a ball lens with radius of curvature r is given by 1/f=(n-1){1/r1+1/r2+t/n (n-1)/r1r2)} where r1= -r2 =r and t=2r. If ball lens diameter: d=2r=1mm, and n=1.57, since f is calculated as 0.713mm, given the range of clear vision D0=250mm, magnification becomes m=D0/f=350 as you noted. Therefore, the magnification of the ball lens is defined in this way. Shigeo
Rubdra, I mistyped refractive index of the ball lens. Correctly, I used n=1.54 in calculating EFL. The formula for EFL is reduced to EFL=f=n D/4(n-1) with D=2r. Shigeo.
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