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oof1231
13.11.2019 •
Mathematics
The intensity of light with wavelength λ traveling through a diffraction grating with n slits at an angle θ is given by i(θ) = n2 sin2(k)/k2, where k = (πnd sin θ)/λ and d is the distance between adjacent slits. a helium-neon laser with wavelength λ = 632.8 × 10−9 m is emitting a narrow band of light, given by −10−6 < θ < 10−6, through a grating with 10,000 slits spaced 10−4 m apart. use the midpoint rule with n = 10 to estimate the total light intensity.
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Ответ:
0.007502795
Step-by-step explanation:
We have
N = 10,000
Replacing these values in the expression for k:
So, the intensity is given by the function
The total light intensity is then
Since
is an even function
and we only have to divide the interval
in five equal sub-intervals
with midpoints ![\bf m_1,m_2,m_3,m_4,m_5](/tpl/images/0371/9098/09bd8.png)
The sub-intervals and their midpoints are
By the midpoint rule
computing the values of I:
Similarly with the help of a calculator or spreadsheet we find
and we have
Finally the the total light intensity
would be 2*0.003751395 = 0.007502795
Ответ:
it goes up by 6 every time
Step-by-step explanation: