Explain how the zeroth-order, first-order, and second-order spectra are produced

Question

Explain how the zeroth-order, first-order, and second-order spectra are produced by the diffraction grating (state the determining conditions). Discuss the path-length differences in terms of the wavelength , the order number, m. How many wavelengths are contained in the path-length difference between the first and third orders? Draw a sketch to ai your explanation. Explain how the different colored spectral lines are formed at higher order and not at zeroth-order. If we had used a laser-light source, what would the higher orders look like? Would it have different colored spectrum? Explain your reasoning. Note: lasers should be used in conjunction with the telescope of a spectrometer, as the focused light ray would absolutely amage the retina; instead, the diffracted laser light should be projected on a screen, as was done in Experiment .

Explanation / Answer

a)Diffraction and interference in waves are the result of reinforcement or cancelation of waves when different waves are at the same point in space at the same time. If the diffraction pattern of the razor's edge is viewed in blue light and then in red light, it is found that the bright and dark bands are closer together in the blue light because its wavelength is shorter. This is one way to confirm the basic theories about the wave nature of light. Example spectrum Diffraction through a series of closely spaced slits (called a grating) serves a useful purpose for the examination of the different wavelengths of light. Diffraction of a narrow beam of light of a single wavelength by a grating will produce a bright beam straight ahead and a series of beams to either side at angles where the light waves from adjacent slits reinforce each other. The first bright image to either side occurs when the difference in the pathlength of the light from adjacent slits of the grating is one wavelength, and it is called the "first order" diffraction maximum. When the pathlength difference is two wavelengths, another bright image occurs (the second order diffraction maximum). If light of a longer wavelength is used, the maxima are at larger angles. When light of multiple wavelengths is used, the different wavelengths(different colors) are separated. The separation of the colors is much larger than that obtained with a prism, so a diffraction grating can be thought of as a "super prism". The gratings to be used in this experiment are transmission gratings which are made by ruling a large number of equally spaced parallel lines on a piece of glass, only a few wavelengths apart. The transparent positions between the lines act as narrow slits. The sketch below compares the spectra produced by a prism and a grating. The experiment involves a careful examination of the spectra (collection of separated wavelengths of light) for several light sources. In each case you are to examine the first order spectrun to the right of the zero angle. The relationship between the wavelength of the light and the angle of diffraction is Wavelength = l = (d/n) sinq where n is the order number, q is the angle of diffraction, and d is the distance between grating lines. For these gratings, there are 600 lines/mm which corresponds to a grating spacing of d = 1670 nanometers. The sine of the angles you measure ( sin q ) B)Diffraction gratings: You can find out what colors a light source is emitting by observing it with a diffraction grating. Diffraction gratings are similar to prisms: they spread light out into its constituent colors. Practice using the diffraction gratings mounted in slides by observing the following objects. Orient the grating so that the colors appear to the left and right of the object you are observing (not above and below). IMPORTANT: Always hold the diffraction grating slide by the edges. Fingerprints on the grating itself will cause damage to the grating. If the gratings appear dirty or smudged, do not wipe them off (which will ruin the grating).

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