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Chapter 20: Q9P (page 525)
Consider a reflection grating operating with an incident angle of 408 in Figure 20-7. (a) How many lines per centimeter should be etched in the grating if the first-order diffraction angle for 600 nm (visible) light is to be 2308? (b) Answer the same question for 1 000 cm21 (infrared) light.
(a)
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A measurement with a signal-to-noise ratio of 100 / 1 can be thought of as a signal, S, with 1 % uncertainty, e. That is, the measurement is.
(a) Use the rules for propagation of uncertainty to show that, if you add two such signals, the result is total signal , giving a signal-to-noise ratio of .
(b) Show that if you add four such measurements, the signal-tonoise ratio increases to 200 / 1.
(c) Show that averaging n measurements increases the signal-to-noise ratio by a factor of compared with the value for one measurement.
Here is an extremely sensitive method for measuring nitrite () down to in natural waters. The water sample is treated with sulfanilamide and N-(1-naphthylethylenediamine) in acid solution to produce a colored product with a molar absorptivity of at 540 nm. The colored solution is pumped into a 4.5-meter-long, coiled Teflon tube whose fluorocarbon wall has a refractive index of 1.29. The aqueous solution inside the tube has a refractive index near 1.33. The colored solution is pumped through the coiled tube. An optical fiber delivers white light into one end of the tube, and an optical fiber at the other end leads to a polychromator and detector.
(a) Explain the purpose of the coiled Teflon tube and explain how it functions.
(b) What is the critical angle of incidence for total internal reflection at the Teflon/water interface?
(c) What is the predicted absorbance of a solution of colored reagent?
(a) What resolution is required for a diffraction grating to resolve wavelengths of 512.23 and 512.26 nm? (b) With a resolution of 104, how close in nm is the closest line to 512.23 nm that can barely be resolved? (c) Calculate the fourth-order resolution of a grating that is 8.00 cm long and is ruled at 185 lines/mm. (d) Find the angular dispersion () between light rays with wavelengths of 512.23 and 512.26 nm for first-order diffraction (n 5 1) and thirtieth-order diffraction from a grating with 250 lines/mm and f 5 3.08.
The exitance (power per unit area per unit wavelength) from a blackbody (Box 20-1) is given by the Planck distribution: where is wavelength, Tis temperature K), his Planck鈥檚 constant, Cis the speed of light, and kis Boltzmann鈥檚 constant. The area under each curve between two wavelengths in the blackbody graph in Box 20-1is equal to the power per unit areaemitted between those two wavelengths. We find the area by integrating the Planck function between wavelengthsand
role="math" localid="1664862982839"
For a narrow wavelength range, the value of is nearly constant and the power emitted is simply the product .
(a) Evaluate and at
(b) Calculate the power emitted per square meter atin the intervalby evaluating the product
(c) Repeat part (b) for the interval
(d) The quantityis the relative exitance at the two wavelengths. Compare the relative exitance at these two wave-lengths atwith the relative exitance at 100K. What does your answer mean?
Explain how beam chopping reduces line noise and noise from source drift.
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