In trying to explain the colored line on a CD or DVD under the skimming light rays of a white lamp,1 we made errors that affect the equations but not the overall conclusions. The mistakes stem from Eq. (1) of Ref. 1. As seen in Fig. 1, in which two parallel light rays coming from the source reflect from point and on the CD (or DVD), the total length of the path from to is (1)
Fig. 1.
Two parallel light rays coming from the source are reflected by a compact disc in and , respectively, at an angle . An observer in is able to see the reflected rays.
Fig. 1.
Two parallel light rays coming from the source are reflected by a compact disc in and , respectively, at an angle . An observer in is able to see the reflected rays.
In Ref. 1, we had divided by rather than multiplying, but this error did not affect our calculations because our later analysis used the approximation . We had also mis-labeled as the length of the segment rather than , which also did not affect our analysis. Finally, we were missing the factor of in determining the total path length. Using this correct expression, the light intensity observed at becomes (2)where N is the (large) number of possible paths that recombine at O.
This expression differs from the corresponding one given in Eq. (8) of Ref. [1], because the arguments of the sine functions include the factor of and have the terms in the numerators rather than denominators. The maxima of the function in Eq. (2) occur at wavelengths , where M is an integer. For a CD, setting and taking , we obtain the following three wavelengths in the visible spectrum: (3)The two odd-numbered wavelengths, λ5 and λ7, were not found in the previous analysis due to the missing factor of . However, even with this correction, we can still understand the observed green color of the light, since the intensity of the light source and the sensitivity of the eye are both much greater for the central wavelength.
For a DVD, setting and taking , we obtain the following wavelengths: (4)In Ref. 1, we were not able to give a good explanation for the observed blue color of the light, since we predicted only the even-numbered wavelengths in the infrared and UV. However, now we can explain this observation.
The later equations in Ref. 1 require similar corrections to the arguments of the sines. These corrections do not affect the qualitative results that were presented. Preliminary spectroscopic investigations confirm that the corrections reported in this erratum agree with observations.
The authors would like to thank Lars Gislén of Lund University for alerting us to these errors.
REFERENCES
1.
R.
De Luca
,
M.
Di Mauro
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O.
Fiore
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A.
Naddeo
, Am. J. Phys.
86
(3
), 169
(2018
).© 2023 Author(s). Published under an exclusive license by American Association of Physics Teachers.
2023
Author(s)