The full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern. (See figure (b).) (a) Does the intensity drop to one-half the maximum value when sin²α = a²/2? (b) Is a = 1.39 rad (about 80°) a solution to the transcendental equation of (a)? (c) Is the FWHM AÐ = 2sin¹(0.442 A/a), where a is the slit width? Calculate the FWHM of the central maximum for slit width (d) 1.17 A, (e) 5.03 A, and (f) 11.7 A. 20 20 Relative intensity 15 10 0.8 0.6 a=2 0.4 0.2 5 05 8 (degrees) (a) 10 15 20 20 Relative intensity 1.0 0.8 0.6 -A0- 0.4 0.2 a= 52 20 15 10 5 0 5 10 15 20 (degrees) (b) (a) (b) (c) > > (d) Number 20 20 Relative intensity 1.0 0.8 06 0.4 0.2 a = 10 15 10 5 0 5 10 15 20 e (degrees) (c) Units (e) Number Units >
The full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern. (See figure (b).) (a) Does the intensity drop to one-half the maximum value when sin²α = a²/2? (b) Is a = 1.39 rad (about 80°) a solution to the transcendental equation of (a)? (c) Is the FWHM AÐ = 2sin¹(0.442 A/a), where a is the slit width? Calculate the FWHM of the central maximum for slit width (d) 1.17 A, (e) 5.03 A, and (f) 11.7 A. 20 20 Relative intensity 15 10 0.8 0.6 a=2 0.4 0.2 5 05 8 (degrees) (a) 10 15 20 20 Relative intensity 1.0 0.8 0.6 -A0- 0.4 0.2 a= 52 20 15 10 5 0 5 10 15 20 (degrees) (b) (a) (b) (c) > > (d) Number 20 20 Relative intensity 1.0 0.8 06 0.4 0.2 a = 10 15 10 5 0 5 10 15 20 e (degrees) (c) Units (e) Number Units >
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:The full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the
pattern where the intensity is one-half that at the center of the pattern. (See figure (b).) (a) Does the intensity drop to one-half the
maximum value when sin²α = a²/2? (b) Is a = 1.39 rad (about 80°) a solution to the transcendental equation of (a)? (c) Is the FWHM AÐ
= 2sin¹(0.442 A/a), where a is the slit width? Calculate the FWHM of the central maximum for slit width (d) 1.17 A, (e) 5.03 A, and (f)
11.7 A.
20
20
Relative intensity
15 10
0.8
0.6
a=2
0.4
0.2
5 05
8 (degrees)
(a)
10 15 20
20
Relative intensity
1.0
0.8
0.6
-A0-
0.4
0.2
a= 52
20
15
10
5 0 5
10
15 20
(degrees)
(b)
Transcribed Image Text:(a)
(b)
(c)
>
>
(d) Number
20
20
Relative intensity
1.0
0.8
06
0.4
0.2
a = 10
15
10
5 0 5
10
15 20
e (degrees)
(c)
Units
(e) Number
Units
>
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