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.

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

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

for b its (t) and c its (d)

step-by-step explanation: