大学物理下课件36 Diffraction

a sin 2 d sin m2
2d m2 a 9.8
Answer: there are five bright fringes are within either of the first side peaks of the diffraction envelope
Diffraction Gratings
the central peak of the diffraction envelope including the
central one.
(b) For second minima of single - slit diffraction :
For double - slit interference :
Solution: (a) For first minima of single - slit diffraction : a sin
For double - slit interference : d sin m2
m2
d a
4.8
Answer: There are nine bright interference fringes are within
Diffraction
Dr. Huaqiu Deng
E-mail: hqdeng@scut.edu.cn
Sample Problem - Single-slit diffraction pattern with white light
Problem: A slit of width a is illuminated by white light. (a) For what value of a will the first minimum for red light of wavelength λ = 650 nm appear at θ = 15°? (b)
(a) For first minimum fringe : a sin
a
sin
650 109 m sin 15o
2.5μm
(b) The first maximum fringe is between the first minimum fringe (a sin θ λ)
and the second minimun fringe (a sin 2)
Resolving power : R avg Nm
Sample Problem - Dispersion and resolving power of a diffraction grating
Problem: A diffraction grating has N = 1.26x104 rulings uniformly spaced over width w = 25.4 mm. It is illuminated at normal incidence by yellow light from a sodium vapor lamp. This light contains two closely spaced emission lines (known as the sodium doublet) of wavelengths 589.00 nm and 589.59 nm. (a) At what angle does the first-order maximum occur (on either side of the center of the diffraction pattern) for the wavelength of 589.00 nm? (b) Using the dispersion of the grating, calculate the angular separation between the two lines in the first order. (c) What is the least number of rulings a grating can have and still be able to resolve the sodium doublet in the first order?
What is the wavelength λ of the light whose first side diffraction maximum is at 15°, thus coinciding with the first minimum for the red light?
Solution:
The first maximum fringe : a sin 1.5'
' a sin (2.5106 m) sin150 430nm
1.5
1.5
Intensity In Single-Slit Diffraction
Intensity :
I
I
0
sin
2
a sin
Intensity minima : I 0 sin 0, 0,
a sin m a sin m, m 1,2,3,
Diffraction By a Double Slit
cos2
I
I0
Fra Baidu bibliotek
cos2
sin
2
a sin , d sin
a : width of slit d : distance between
the centers of the slits
Maxima : d sin m, m 0,1,2,
d : grating spacing
Half width of the lines :
hw
Nd
cos
Gratings Spectroscope
Dispersion : D m d cos
∆θ: angular separation of two lines whose wavelengths differ by ∆λ.
sin
2
cos2
sin
2
Sample Problem - Double-slit experiment
with diffraction of each slit included
Problem: In a double-slit experiment, the wavelength λ of the light source is 405 nm, the slit separation d is 19.44 μm, and the slit width a is 4.050 μm. Consider the interference of the light from the two slits and also the diffraction of the light through each slit. (a) How many bright interference fringes are within the central peak of the diffraction envelope? (b) How many bright fringes are within either of the first side peaks of the diffraction envelope?