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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?

Short Answer

Expert verified

The number of grooves that are illuminated and the diffraction order increases the resolution of a grating.

Step by step solution

01

Step: 1 Define the grating:

Diffraction grating is a series of clusters used to separate an incident wave into its wavelength by directly separating the magnitude of the diffraction.

02

Step: 2 The variables which increase the resolution of a grating:

The number of grooves that are illuminated and the diffraction order increases the resolution of a grating.

03

Step: 3 The variables which increase the dispersion of the grating:

The diffraction order increase the dispersion of the grating, while the spacing between lines in the grating is inversely proportional to dispersion of the grating.

04

Step: 4 The blaze angle chosen to optimize a grating:

The blaze angle chosen to optimize a grating for a particular wavelength is selected to give specular reflection at desired diffraction angle.

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Most popular questions from this chapter

Explain how a laser generates light. List important properties of laser light.

The interferometer mirror of a Fourier transform infrared spectrophotometer travels pm1 cm .

(a) How many centimeters is the maximum retardation,∆ ?

(b) State what is meant by resolution.

(c) What is the approximate resolution (cm‐1)of the instrument?

(d) At what retardation interval,∆ , must the interferogram be sampled (converted into digital form) to cover a spectral range of 0 to 2000 cm-1 ?

The photograph of upconversion in Color Plate 21shows total internal reflection of the blue ray inside the cuvet. The angle of incidence of the blue ray on the wall of the cuvet is~55°. We estimate that the refractive index of the organic solvent is 1.50and the refractive index of the fused-silicacuvet is 1.46. Calculate the critical angle for total internal reflection at the solvent/ silica interface and at the silica/air interface. From your calculation, which interface is responsible for total internal reflection in the photo?

The variation of refractive index, n, with wavelength for fused silica is given by

n2‐1=(0.6961663)λ2λ2‐(0.0684043)2+(0.4079426)λ2λ2‐(0.1162414)2+(0.8974794)λ2λ2‐(9.896161)2

where λ is expressed in μm.

(a) Make a graph of n versus λ with points at the following wavelengths: 0.2,0.4,0.6,0.8,1,2,3,4,5, and 6μm.

(b) The ability of a prism to spread apart (disperse) neighboring wavelengths increases as the slope dn/dλincreases. Is the dispersion of fused silica greater for blue light or red light?

(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 (ϕ∆) 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.
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