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Experiment: Glas Ball Rainbow

glass ball rainbow experiment

The light source used was slide projector with halogen lamp.

To determine the refractive index of the glass ball (D=70 mm), the effective focal length f from the center and the back focal length fb were measured (f = fb+D/2).

glass ball focal length
 focal length formula

formula refractive index

(*)

The result obtained for the index of refraction is n = 1.52 ± 0.02.

The supplier of the sphere specifies the material as  borosilicate glass. Searching on the internet:

n
 nm
1.474 589 (1)
1.514 632.8 (2)
1.473 546.1 (3)
1.473 587.6 (4)

09-1604_SCHOTT_Boroloat33_GB.pdf

The rainbow angle δ of the photo can be calculated, reducing the measured distance L and diameter D of the rainbow by means of the applet:


experiment rainbow


δ = arctan [(D/2-y)/(L-x)]

Result (5 experiments):
n
 δmax stand. dev.
 applet
1.520
 20.3°
 ± 0.3°
 19.3°
1.473
 19.7°
 ± 0.5
 24.3°
1.486
 19.9°
 ± 0.4°
 22.9°

The refractive index n is used to compute the point (x|y) which is necessary to reduce the measured distances L and D.

Pernter, in his book, mentions a rainbow angle of 22° 51' = 22.85° for glass.

The applet may be used to calculate the refractive index of the glass from the rainbow angle measured by my experiments:

refractive index rainbow angle

The result is nglass = 1.510 ± 0.003, instead of 1.52 by the focal length.



Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region

Web Links
(*) Understanding Ball Lenses (Edmund Optics)

Borosilicate Glass
The International Association for the Properties of Water and Steam
Books
Pernter, J. M., Exner, F. M.: Meteorologische Optik; Salzwasser Verlag, Paderborn, 2012; 978-3-86444-515-6;
Nachdruck der 2. Auflage 1922.

Pernter, J. M., Exner, F. M.: Meteorologische Optik; Wilhelm Braumüller, Wien und Leipzig, 2. Aufl. 1922.


2016 J. Giesen

updated: 2016, Apr 28