Abstract

An interesting optical focusing effect occurred in the early heating phases of a simple model of a lava lamp that was constructed to demonstrate convection effects. During this early heating phase, the interface between the two immiscible liquids was found to form a surface of rotation with a conic cross section that acted as a mirror to produce an excellent image of the filament of the bulb within the lower liquid. The relevant features of the lamp construction are discussed briefly, and photographs of this focusing effect are shown. A simple analysis is presented that transforms the photographed cross section of the liquid interface into the true cross section by removing the effect of the cylindrical lens formed by the fluid-filled bottle, and the resulting cross section is then fitted to the shape of an ellipse. The possible cause for the shape of this liquid interface is discussed and compared and contrasted with the somewhat analogous situation of a stretched circular membrane that is subjected to different gas pressures on either side of the membrane.

© 2011 Optical Society of America

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References

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  1. K. K. Karukstis and G. R. van Hecke, Chemistry Connections: The Chemical Basis of Everyday Phenomena, 2nd ed.(Academic, 2003).
  2. B. Gyure and I. M. Janosi, “Basics of lava-lamp convection,” Phys. Rev. E 80, 046307 (2009).
    [CrossRef]
  3. O. G. Sutton, Understanding Weather (Penguin, 1960).
  4. A. V. Getling, Rayleigh–Benard Convection (World Scientific, 1998).
  5. N. F. Comins and W. J. Kaufmann, Discovering the Universe (2012), pp. 319–320.
  6. J. C. Muirhead, “Variable focal length mirrors,” Rev. Sci. Instrum. 32, 210–211 (1961).
    [CrossRef]
  7. H. Shimizu, “Ultralightweight reflector for lidar applications,” Appl. Opt. 25, 1467–1469 (1986).
    [CrossRef] [PubMed]
  8. R. V. Southwell, An Introduction to the Theory of Elasticity for Engineers and Physicists, 2nd ed. (Oxford Univ. Press, 1941).
  9. N. K. Adam, The Physics and Chemistry of Surfaces (Dover, 1968), pp. 8–10.

2009

B. Gyure and I. M. Janosi, “Basics of lava-lamp convection,” Phys. Rev. E 80, 046307 (2009).
[CrossRef]

1986

1961

J. C. Muirhead, “Variable focal length mirrors,” Rev. Sci. Instrum. 32, 210–211 (1961).
[CrossRef]

Adam, N. K.

N. K. Adam, The Physics and Chemistry of Surfaces (Dover, 1968), pp. 8–10.

Comins, N. F.

N. F. Comins and W. J. Kaufmann, Discovering the Universe (2012), pp. 319–320.

Getling, A. V.

A. V. Getling, Rayleigh–Benard Convection (World Scientific, 1998).

Gyure, B.

B. Gyure and I. M. Janosi, “Basics of lava-lamp convection,” Phys. Rev. E 80, 046307 (2009).
[CrossRef]

Janosi, I. M.

B. Gyure and I. M. Janosi, “Basics of lava-lamp convection,” Phys. Rev. E 80, 046307 (2009).
[CrossRef]

Karukstis, K. K.

K. K. Karukstis and G. R. van Hecke, Chemistry Connections: The Chemical Basis of Everyday Phenomena, 2nd ed.(Academic, 2003).

Kaufmann, W. J.

N. F. Comins and W. J. Kaufmann, Discovering the Universe (2012), pp. 319–320.

Muirhead, J. C.

J. C. Muirhead, “Variable focal length mirrors,” Rev. Sci. Instrum. 32, 210–211 (1961).
[CrossRef]

Shimizu, H.

Southwell, R. V.

R. V. Southwell, An Introduction to the Theory of Elasticity for Engineers and Physicists, 2nd ed. (Oxford Univ. Press, 1941).

Sutton, O. G.

O. G. Sutton, Understanding Weather (Penguin, 1960).

van Hecke, G. R.

K. K. Karukstis and G. R. van Hecke, Chemistry Connections: The Chemical Basis of Everyday Phenomena, 2nd ed.(Academic, 2003).

Appl. Opt.

Phys. Rev. E

B. Gyure and I. M. Janosi, “Basics of lava-lamp convection,” Phys. Rev. E 80, 046307 (2009).
[CrossRef]

Rev. Sci. Instrum.

J. C. Muirhead, “Variable focal length mirrors,” Rev. Sci. Instrum. 32, 210–211 (1961).
[CrossRef]

Other

K. K. Karukstis and G. R. van Hecke, Chemistry Connections: The Chemical Basis of Everyday Phenomena, 2nd ed.(Academic, 2003).

R. V. Southwell, An Introduction to the Theory of Elasticity for Engineers and Physicists, 2nd ed. (Oxford Univ. Press, 1941).

N. K. Adam, The Physics and Chemistry of Surfaces (Dover, 1968), pp. 8–10.

O. G. Sutton, Understanding Weather (Penguin, 1960).

A. V. Getling, Rayleigh–Benard Convection (World Scientific, 1998).

N. F. Comins and W. J. Kaufmann, Discovering the Universe (2012), pp. 319–320.

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Figures (8)

Fig. 1
Fig. 1

Diagram of the lava lamp arrangement.

Fig. 2
Fig. 2

Photograph of the wine bottle lava lamp.

Fig. 3
Fig. 3

Several views of the image of the filament taken from different angles.

Fig. 4
Fig. 4

Comparison of the lamp filament photograph with the image produced within the lava lamp.

Fig. 5
Fig. 5

Measured image of the liquid surface.

Fig. 6
Fig. 6

Optical path diagram. Cross section of the liquid-filled bottle, showing a dashed line that depicts the path of the light from a point T to the camera, passing through the liquid and the glass wall of the bottle.

Fig. 7
Fig. 7

Comparison of the measured shape of the liquid interface with the shape corrected for the distortion produced by the cylindrical lens of the liquid-filled bottle.

Fig. 8
Fig. 8

Comparison of the shape of the liquid interface cross section with that of an ellipse.

Equations (2)

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θ = tan 1 ( a d ) .
y 2 = b 2 a 2 ( 2 a x x 2 ) ,

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