Page:Elementary Text-book of Physics (Anthony, 1897).djvu/451

§356] $$\sin \theta$$ becomes $$\frac{2\lambda}{2d} = \frac{\lambda}{d}; \, \frac{4\lambda}{2d} = \frac{2\lambda}{d},$$ etc., and satisfies the equation $$\sin \theta = \frac{n\lambda}{d},$$ which expresses the condition under which light is all destroyed. Hence in this case all the spectra of even orders fail. Moreover, the spectra after the first are not brilliant. When $$f$$ equals $$2d$$ the spectrum of the third order fails.

356. Measurement of Wave lengths.—To realize practically the conditions assumed in the theoretical discussion of the last section, some accessory apparatus is required. It has been assumed that the wave incident upon the grating was plane. Such a wave would proceed from a luminous point or line at an infinite distance. In practice it may be obtained by illuminating a very narrow slit, taking it as the source of light, and placing it in the principal focal plane of a well-corrected converging lens. The plane wave thus obtained passes through the grating, or is reflected from it, and is received on a second lens similar to the first, which gives an image either on a screen or in front of an eyepiece, where it is viewed by the eye. The general construction of the apparatus may be inferred from Fig. 131. It is called the spectrometer.

$$A$$ is a tube carrying at its outer end the slit and at its inner end the lens, called a collimating lens. $$CD$$ is a horizontal graduated circle, at the centre of which is a table on which the grating is mounted, and so adjusted that the axis of the circle lies in its plane and parallel to its lines. In using a reflecting grating the collimating and observing telescopes may be fixed at a constant angle $$2\beta$$ with each other, which may be determined once for all in making the adjustments of the instrument. To determine this angle the grating is turned until light thrown through the observing telescope upon the grating is reflected back on itself. The position of the graduated circle is then read. The difference between this