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Unformatted text preview: Biconvex Lens  Circle of Least Confusion A biconvex lens is used to focus a plane wave that is propagating on—axis (light
traveling parallel to the axis of lens). The lens has a 32 mm diameter with n = 1.5. The
magnitudes of the radii of curvature of the surfaces are R1 = 50 mm and R2 = 50 mm. This lens and this conﬁguration are shown in the attached ﬁgure. Incident rays close to the axis of the lens (h —> 0) focus at the paraxial ray focal
point. From the paraxial focal point back toward the lens, incident rays at successively
larger distances (h) from the axis of the lens focus closer to the lens. The tangents of
these rays form what is known as the caustic surface. The caustic surface is a smooth
surface starting from the paraxial ray focus and extending back toward the lens. There
is a caustic surface above the axis of the lens and a caustic surface below the axis of the
lens. Along the axis of the lens the minimum diameter disk of focused light is the circle
of least confusion. It occurs where the marginal ray (largest value of h) intersects the caustic surface. An aperture stop is now placed immediately in front of this lens (to the left of
the lens as shown in the ﬁgure). As the diameter of the aperture stop is decreased, the
value of h for the marginal ray correspondingly decreases. Ignoring diffraction effects,
determine by graphical means for this lens the range of fnumbers which produce a circle
of least confusion of 1.0mm or less. Use the paraxial ray focal length in evaluating the fnumber. Show all work. Put your answer in the space provided. Range of f—numbers: < f — no. < BICONVEX LENS A biconvex lens has radii of curvature of R1 and R2, a center thickness of d, and
an index of refraction n. If R1 and R2 are taken to be magnitudes, the focal distance of this biconvex lens in air for an axial ray of distance h from the principal axis is f = {m +112 _ d)  Mia3%)} + 53/
mum1%) (RI +R2 — d) sinlsin‘l(%) ‘ ($29] + 3%»
_(sml{ (1%) (R1 + 32  d) mun1%)  (xi1)] + flab
+[Sm—Ie>—ml<a—i>n}w 5mm Fig. 1. Focusing of rays by biconvex lens showing spherical aberration. Biconvex Lens  Circle of Least Confusion A 1.00 mm diameter circle of least confusion occurs at a focal distance of about f =
44 mm. ’ For this circle of least confusion, the marginal ray that intersects the caustic surface is at about h 2 14mm. For this marginal ray, the f—no. is
fno. = f(paraxial)/(2)(14 mm) = 50 mm/28 mm = 1.785 For larger f—nos., the circle of least confusion is even smaller. ...
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 Spring '08
 Gaylord
 Geometrical optics, biconvex lens

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