Learning Materials
Features
Discover
Chapter 20: Q4P (page 525)
Which variables increase the resolution of a grating? Which variables increase the dispersion of the grating? How is the blaze angle chosen to optimize a grating for a particular wavelength?
The number of grooves that are illuminated and the diffraction order increases the resolution of a grating.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
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’s constant, Cis the speed of light, and kis Boltzmann’s 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?
(a) In the cavity ring-down measurement at the opening of this chapter, absorbance is given by whereis the length of the triangular path in the cavity, Cis the speed of light, Tis the ring-down lifetime with sample in the cavity, and is the ring-down lifetime with no sample in the cavity. Ring-down lifetime is obtained by fitting the observed ring-down signal intensityto an exponential decay of the form , whereis the initial intensity and t is time. A measurement ofis made at a wavelength absorbed by the molecule. The ring-down lifetime for 21.0-cm-1 along empty cavity is andfor a cavity containing.role="math" localid="1664865078479" Find the absorbance ofat this wavelength.
(b) The ring-down spectrum below arises from and from of methane in outdoor air at 0.13. The spectrum arises from individual rotational transitions of the ground vibrational state to a second excited C-H)vibrational state of the molecule. (i) Explain what quantity is plotted on the ordinate ( Y-axis). (ii) The peak foris at. What is the wavelength of this peak in? What is the name of the spectral region where this peak is found?
(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.
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.
Refer to the Fourier transform infrared spectrum in Figure 20-33.
(a) The interferogram was sampled at retardation intervals of. What is the theoretical wavenumber range (0 to ?) of the
spectrum?
(b) A total of 4 096 data points were collected from . Compute the value of, the maximum retardation.
(c) Calculate the approximate resolution of the spectrum.
(d) The interferometer mirror velocity is given in the figure caption. How many microseconds elapse between each datum?
(e) How many seconds were required to record each interfero gram once?
(f) What kind of beam splitter is typically used for the region 400 to 4 000? Why is the region below 400not observed?
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App