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Problem

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question

The intensity of light with wavelength λ\lambda traveling through a diffraction grating with NN slits at an angle θ\theta is given by I(θ)=N2sin2k/k2I(\theta)=N^2 \sin ^2 k / k^2, where k=(πNdsinθ)/λk=(\pi N d \sin \theta) / \lambda and dd is the distance between adjacent slits. A helium-neon laser with wavelength $\lambda=632.8 \times 10^{-9} \mathrm{~m}$ is emitting a narrow band of light, given by −10−6<θ<10−6-10^{-6}<\theta<10^{-6}, through a grating with 10,000 slits spaced $10^{-4} \mathrm{~m}$ apart. Use the Midpoint Rule with n=10n=10 to estimate the total light intensity ∫−10−610−6I(θ)dθ\int_{-10^{-6}}^{10^{-6}} I(\theta) d \theta emerging from the grating.
Plain-text mathematical notation (without MathML)
The intensity of light with wavelength λ traveling through a diffraction grating with N slits at an angle θ is given by I(θ)=N²sin²k/k², where k=(πNdsinθ)/λ and d is the distance between adjacent slits. A helium-neon laser with wavelength $\lambda=632.8 \times 10^{-9} \mathrm{~m}$ is emitting a narrow band of light, given by −10^(−6)<θ<10^(−6), through a grating with 10,000 slits spaced $10^{-4} \mathrm{~m}$ apart. Use the Midpoint Rule with n=10 to estimate the total light intensity ∫_(−10^(−6))^(10^(−6))I(θ)dθ emerging from the grating.
Original LaTeX notation
The intensity of light with wavelength $\lambda$ traveling through a diffraction grating with $N$ slits at an angle $\theta$ is given by $I(\theta)=N^2 \sin ^2 k / k^2$, where $k=(\pi N d \sin \theta) / \lambda$ and $d$ is the distance between adjacent slits. A helium-neon laser with wavelength $\lambda=632.8 \times 10^{-9} \mathrm{~m}$ is emitting a narrow band of light, given by $-10^{-6}<\theta<10^{-6}$, through a grating with 10,000 slits spaced $10^{-4} \mathrm{~m}$ apart. Use the Midpoint Rule with $n=10$ to estimate the total light intensity $\int_{-10^{-6}}^{10^{-6}} I(\theta) d \theta$ emerging from the grating.

category

math

options

  1. 72.3
  2. 92.7
  3. 38.5
  4. 76.9
  5. 51.2
  6. 59.4
  7. 45.6
  8. 67.9
  9. 24.8
  10. 83.1

src

scibench-calculus

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Source and history

upstream_id / Original problem ID
8633
task_id
84a6c75c-b22f-55ae-8edb-69bde93dd24e
task_key
default--test--8633
task_revision_id
1
config / split
default / test

Official source

initial import