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Unformatted text preview: Plano  Convex Lens A plano—convex lens has a radius of curvature of R and an index of refraction n.
A collimated beam of light of wavelength A is incident upon the plano side of this lens in air as shown in the ﬁgure. 1) For a planoconvex lens with R = 25 mm, n = 1.5, and 32 mm in diameter, calculate
the focal length of this lens in the paraxial ray approximation. Express your answer in mm and put it in the space provided.
fparamial : mm 2) Accounting for the shape of the plane—convex lens, show that the focal distance as deﬁned in the ﬁgure, for an axial ray of distance h from the principal axis is f = [h/tan[sin_1(7—11?h> — sin_1<%>]] _ R+ (R2 _ h2)1/2 3) Show that this trigonometric expression for the focal distance reduces to the paraxial ray expression for the focal length (used above) as h approaches zero. 4) Calculate the focal distance for the case when h = 5 mm, 7.5 mm, 10 mm, 12.5 mm,
and 15 mm. Draw these rays on the ﬁgure and show their intersection with the princi— pal axis. The distance between neighboring tick marks is 5 mm. Insert your calculated values in the table below. h(mm) f(_mnll
5.0 7.5 10.0 12.5 15.0 5) On the ray tracing diagram indicate the circle of least confusion. Determine the focal
distance (as deﬁned in the ﬁgure) for the circle of least confusion. Express your answer in mm and put it in the space provided.
fc.o.l.c. 2 mm Determine the diameter of the circle of least confusion. Express your answer in mm and put it in the space provided. Dc.0.l.c. : mm 6) For a wavelength of A = 632.8 nm, calculate, showing all work, the focused spot size
for a diffractionlimited lens having a focal length equal to the focal distance of the circle
of least confusion determined above and having the same diameter as the piano—convex lens described above. Express your answer in um and put it in the space provided. Ddiffraction—limited = ,um Calculate, how many times larger the circle of least confusion is in comparison to the
diffraction—limited spot size. Express your answer as a ratio and put it in the space pro—
vided. ' Dc.o.l.c. Ddiffraction— limited 7) Why does the diffraction—limited spot size fail to give the diameter as determined from geometrical optics? Plano  Convex Lens 1) 712 = 1.5, n1 = 1.0, R1 = 00, R2 = —25mm .1. _ "2—”1(i__1_) f— m R1 R2 f = n1R2 = 50mm
712—721 2) oz : sin—16%) ﬂ = sin—1 (11.22) R2
tan(,6 — a) = %
t= R2  \/R§——h—2
f= [h/tan[sin_l(%§> — sin—1(Ri2>]] — R2 + (R22) — h2)1/2' 3) In the paraxial ray approximation . ngh h h R2
1 =ht ——— =—=
#36 f /‘m(R2 R2) ”xii—1% n2—1 4) For M = 1.5 and R2 2 25mm
h(mm) f(mm)
5.0 47.7
7.5 44.7
10.0 40.2
12.5 33.8
15.0 24.1 kl\\ 22:23:12: 1 5) Circle of least confusion fc.o.l.c = 289 mm Dc.o.l.c : 56mm 6) Diffraction—limited spot size (x\ = 632.8 nm) 4A1”
Dd_l = :lT—l), = 0.7277/1771
Dc at c
' ' = 7696
Dd—l 7) The diffractionlimited spot size is achieved only when geometrical optics predicts a zero spot size or a spot size that is very small compared to the diffractionlimited spot
size. ...
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 Spring '08
 Gaylord

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