?The intensity of light with wavelength \(\lambda\) traveling through a diffraction

Chapter 7, Problem 43

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The intensity of light with wavelength \(\lambda\) traveling through a diffraction grating with \(N\) slits at an angle \(\theta\) is given by \(I(\theta)=\left(N^{2} \sin ^{2} k \right) / k^{2}\), where \(k=(\pi Nd \ \sin \theta) / \lambda\) and \(d\) is the distance between adjacent slits. A helium-neon laser with wavelength \(\lambda=632.8 \times 10^{-9} \ m\) is emitting a narrow band of light, given by \(-10^{-6}<\theta<10^{-6}\), 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 \(\int_{-10}^{10^{-6}} I(\theta) \ d \theta\) emerging from the grating.

Equation Transcription:

N

I() = (N2 sin2 k)/k2

k = (Nd sin )/

d

= 632.8 x 10-9 m

-10-6 <  < 10-6

10-4 m

n = 10

∫ I () d

Text Transcription:

lambda

N

theta

I(theta) = N^2 sin^2 k)/k^2

k = (pi Nd sin theta)/lambda

d

lambda = 632.8 x 10_-9 m

-10_-6 < theta < 10_-6

10_-4 m

n = 10

integral _-10 ^10^-6 I(theta) d theta