Abstract

An innovative nondestructive technique for mesuring the refractive index of a simple lens is described. The proposed method is superior to existing ones because the focusing error and the spherical aberrations are reduced. Apart from this, the strength parameters (i.e., r1 and r2) of a lens are not required at all since the derived lens-index formula is independent of the lens's physical parameters. The shearing interferometric technique is a sensitive aid for detecting the focal plane of the test lens. A modified criterion for determining the focal length has been used. In this case two miscible liquids or compounds are not necessary. The well-known liquid immersion method is the particular case of this technique. The Murty shearing interferometer has been used as an optical device to observe the defocusing defect in the form of fringes. The amount of defocusing is easily calculated. An equation for this error has been theoretically deduced and experimentally verified. The technique described is quick to perform and easy in handling. The various effects due to the lens's aperture and aberrations, thickness of the glass cell, liquid column, etc. are also discussed. For N liquids, there are N (N − 1)/2 ways of calculating the lens′s index. Owing to its nature this is termed the nondestructive nonmiscible-liquid immersion technique for index measurement of a lens.

© 1983 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Bergmann, C. Schaefer, Lehrbuch der Experimental Physik Band III Optik (Walter de Gruyter, Berlin, 1978), p. 416.
  2. G. Smith, Appl. Opt. 21, 755 (1982).
    [CrossRef] [PubMed]
  3. M. V. R. K. Murty, Appl. Opt. 3, 531 (1964).
    [CrossRef]
  4. W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, London, 1974), p. 74.

1982 (1)

1964 (1)

Bergmann, L.

L. Bergmann, C. Schaefer, Lehrbuch der Experimental Physik Band III Optik (Walter de Gruyter, Berlin, 1978), p. 416.

Murty, M. V. R. K.

Schaefer, C.

L. Bergmann, C. Schaefer, Lehrbuch der Experimental Physik Band III Optik (Walter de Gruyter, Berlin, 1978), p. 416.

Smith, G.

Welford, W. T.

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, London, 1974), p. 74.

Appl. Opt. (2)

Other (2)

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, London, 1974), p. 74.

L. Bergmann, C. Schaefer, Lehrbuch der Experimental Physik Band III Optik (Walter de Gruyter, Berlin, 1978), p. 416.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Optical arrangement for observing defocusing and for measuring the exact focal length of the test lens.

Fig. 2
Fig. 2

Photographs.showing defocusing of a lens in air.

Fig. 3
Fig. 3

Photographs showing defocusing of a lens immersed in water inside the glass cell.

Fig. 4
Fig. 4

Parameters involved in determining the exact focal length.

Tables (5)

Tables Icon

Table I Lens in Air; Focal Length of the Test Lens in Air = 232.28 mm

Tables Icon

Table II Lens in Water; Focal Length of the Test Lens in Water = 844.53mm

Tables Icon

Table III Ways of Calculating the Index of a Lens

Tables Icon

Table IV Measured Focal Length

Tables Icon

Table V Calculated Lens Index

Equations (54)

Equations on this page are rendered with MathJax. Learn more.

( 1 / f ) = ( n n L ) ( 1 / r 1 1 / r 2 ) + ( n n L ) 2 d / r 1 r 2 n ,
( 1 / f 1 ) = ( n n 1 ) ( 1 / r 1 1 / r 2 ) + ( n n 1 ) 2 d / r 1 r 2 n ,
( 1 / f 2 ) = ( n n 2 ) ( 1 / r 1 1 / r 2 ) + ( n n 2 ) 2 d / r 1 r 2 n ,
O = n 2 [ ( 1 + K ) ( f 1 f 2 ) ] n ( 1 + 2 K ) ( n 1 f 1 n 2 f 2 ) + K ( n 1 2 f 1 n 2 2 f 2 ) ,
K = d / ( r 2 r 1 ) .
n = ( n 2 f 2 n 1 f 1 ) ( f 2 f 1 ) [ ( 1 β ) ] ,
β = 0.5 ( r 2 r 1 ) ( r 2 r 1 + d ) [ 1 + 1 + d ( r 2 r 1 + d ) f 1 f 2 4 ( n 2 n 1 ) 2 ( r 2 r 1 ) 2 ( n 2 f 2 n 1 f 1 ) 2 ] .
β = r / ( 2 r d ) [ 1 + 1 d ( 2 r d ) f 1 f 2 ( n 2 n 1 ) 2 r 2 ( n 2 f 2 n 1 f 1 ) 2 ] .
N = ( n i f i n j f j ) ( f i f j ) [ ( 1 + β ij ) ] ,
n = ( n i f i n j f j ) ( f i f j ) .
Δ n = n [ { n i ( n i f i n j f j ) 1 ( f i f j ) } Δ f i + { n j ( n i f i n j f j ) 1 ( f i f j ) } Δ f j ] .
Δ f = λ f 2 / 2 s Δ X ,
Δ f = 1 2 ( λ / s ) ( N / S ) f 2 .
Δ f = f 2 ( 1 / r 1 1 / r 2 ) Δ n .
Δ n = 1 2 ( λ / s ) ( N / S ) r 1 r 2 / ( r 2 r 1 ) .
Δ n = 1 2 ( λ / s ) ( N / S ) r .
s = d sin 2 ω / n 2 sin 2 ω ,
f = s f + t G / n G + t L / n L + s p ,
s p = ( t / n ) [ ( 1 r 2 / r 1 ) 1 ] .
s p = t / n .
s p = t / 2 n .
n ij = ( n i f i ) liquid L i ( n j f j ) liquid L j ( f i ) liquid L i ( f j ) liquid L j .
A _ +
B _ +
C _ +
D _ +
E _ +
F _ +
G _ ±
A _
B _
C _
D _
E _
F _
A _ +
B _ +
C _ +
D _ +
E _ +
F _ +
G _ ±
A _
B _
C _
D _
E _
F _
L 5 L N
n 15 n 1 N
n 25 n 2 N
n 35 n 3 N
n 45 n 4 N
n 55 n 5 N n N 5 n N N

Metrics