## Abstract

Measurements of lens parameters such as focal length, radius of curvature, and refractive index are important. We describe a measurement method that utilizes a Michelson interferometer to determine parameters of thin, convex lenses. The real fringe system formed by a Michelson interferometer is used to determine the focal lengths and the radii of curvature of the lenses. The refractive index of the lens material is determined from the thin-lens formula. We were able to determine the refractive indices to an accuracy as great as 99.97\%. A detailed theoretical and experimental analysis is given.

© 2006 Optical Society of America

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### Equations (47)

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(4)
$$\Delta x={R}_{1}-{R}_{2}=2d\text{\hspace{0.17em}}\mathrm{cos}\left(\theta \right),$$
(5)
$$d={l}_{2}-{l}_{1}$$
(10)
\left({l}_{2}-{l}_{1}=d=0\right)
(13)
\left({l}_{2}-{l}_{1}=d\ne 0\right)
(14)
0.01\text{\hspace{0.17em} mm}
(23)
$$R\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{y}_{2}-{y}_{1}.$$
(24)
$$n=1+\frac{{R}_{1}{R}_{2}}{f\left({R}_{2}-{R}_{1}\right)},$$
(28)
$$\mathrm{d}n=\pm \left(\frac{\mathrm{d}R}{2f}-\frac{R}{2{f}^{2}}\text{\hspace{0.17em}}\mathrm{d}f\right).$$
(29)
$$\mathrm{d}n=\pm \left[\frac{\mathrm{d}R}{2f}-\frac{\left(n-1\right)}{2f}\text{\hspace{0.17em}}\mathrm{d}f\right]\mathrm{.}$$
(30)
f=400\text{\hspace{0.17em} mm}
(31)
\mathrm{d}f=0.14\text{\hspace{0.17em} mm}
(32)
\mathrm{d}R\phantom{\rule[-0.0ex]{0.25em}{0.0ex}}=\phantom{\rule[-0.0ex]{0.25em}{0.0ex}}0.18\text{\hspace{0.17em} mm}
(33)
n\phantom{\rule[-0.0ex]{0.25em}{0.0ex}}=\phantom{\rule[-0.0ex]{0.25em}{0.0ex}}1.51509
(34)
632.8\text{\hspace{0.17em} nm}
(35)
\mathrm{d}n=\pm 0.0002
(36)
10\text{\hspace{0.17em} mW}
(37)
632.8\text{\hspace{0.17em} nm}
(39)
2.5\text{\hspace{0.17em} cm}
(40)
200\text{\hspace{0.17em} mm}
(41)
\left(\Delta f\right)
(42)
({R}_{w}={f\phantom{\rule[-0.0ex]{0.25em}{0.0ex}}}^{2}/\Delta f;\text{\hspace{0.17em}}{R}_{w}
(43)
500\text{\hspace{0.17em} mm}
(44)
2.5\text{\hspace{0.17em} cm}
(45)
200\text{\hspace{0.17em} mm}