Sir J. Herschel
Lacock Abbey, Chippenham
4 Feb/48
Dear Sir
In your Treatise on Light <1> p. 489 you have discussed Fraunhofer’s <2> important observations on the perfect spectra produced by diffraction through his gratings – especially the remarkable fact, that when the incident light is inclined to the grating, the spectra on each side of the axis are not equidistant from it, but very much the contrary – It is evident that this is an experimentum crucis to test any theory – a theory which explains it accurately cannot be far from the truth – So Fraunhofer himself thought, see p. 355 of his Kurzer Bericht &c. <3> – At page 490 you give Fraunhofer’s formula expressive of the law of the phenomena but without any proof. On referring to Fraunhofer’s work I see he has given no proof himself, but merely says that he has entwickelt <4> or deduced it from the Theory of Interference proposed by Young <5> [p. 358] – Now the question which I wish to ask is whether this is to be considered as an undemonstrated theorem of Fraunhofer’s or whether it is a thing demonstrated & admitted by writers on the undulatory theory. I have long entertained some peculiar views, as I believe, on the Theory of Light. I remember conversing with Fraunhofer himself on the subject and asking him whether he could explain the fact of the fixed lines being visible in the spectra produced by gratings, or in other words of the spectrum being reduced to a point for each homogenous ray of light. He told me that he could, but I am not aware that he ever published his demonstration –
Lately I thought I would try whether the undulatory theory, according to my notions of it, sufficed to explain the fact of the spectra produced by an inclined grating being unequally remote from the axis; being as I said before, a rigorous test of the truth of any theory. Accordingly I selected the two observations quoted by you p. 489 where the grating was inclined 55°, and the discordance of the spectra on the 2 sides of the axis was such that one of them was deviated more than twice as much as the other, and yet the fixed lines remained visible. Having referred to Fraunhofer’s work, I find that his observation of the deviations was as follows – page 356
| On one side of the Axis | 15° | 6' | 36" |
| On the other – | 30 | 33 | 10 |
Now I have calculated rigorously what the deviation ought to be by the undulatory Theory of Light, and I find
| deviation of first Ray | 15° | 6' | 37" |
| Fraunhofer’s observatn | 15 | 6 | 36 |
| Error | 1 |
| deviation of Second Ray | 30° | 33' | 20" |
| F’s observatn | 30 | 33 | 10 |
| error | 10 |
The agreement with Theory much exceeds what I expected. In the same page Fraunhofer gives several more measurements which I should like also to calculate, but as perhaps I am only doing what has been already done I should be glad to know whether you think that it is a matter of importance only so much has been written on the undulatory Theory which I never read, that perhaps this very point may have been already discussed and admitted as one of the proofs of the Theory –
Believe me yours very truly
H. F. Talbot
Notes:
1. John Frederick William Herschel wrote his article ‘Light’, in 1827. By 1828 some form of printed copy was available, including the Plates 1–14. The article appeared in the 1830 volume of Encyclopaedia Metropolitana, 2nd Division: Mixed Sciences, v.2, 1830, pp.341–586.
2. Joseph von Fraunhofer (1787–1826), optician, Munich.
3. Joseph von Fraunhofer, Kurzer Bericht von den Resultaten neuerer Versuch, über die Gesetze des Lichtes, und die Theorie derselben, (Leipzig: 1823).
4. developed
5. Thomas Young (1773–1829), natural philosopher.