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Diffraction of light: maximums by Grating

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An array of many identical slits placed close together with uniform spacing is called a grating.

In a particular grating the slits are narrow enough to diffract the light passing through into a broad wavefront. The waves coming from the many slits interfere, producing bright spots on the screen wherever all these waves arrive in phase.

The slide containing the grating in the laser beam is mounted, the set-up is adjusted to produce a bright red diffraction pattern.

You mark the positions of the central maximum and of three diffraction maximums on either side of it. Then you can measure the distances (x1, x2, x3, ....) of the maximums from the central maximum. What would be reasonable estimates for these values?

Estimate the distance L from the grating to the screen; this will allow you to calculate the diffraction angle θ for each maximum (tan theta; n = xn/L).

How would you calculate a value for the wavelength lambda; of the laser light for each of your angles theta; n?

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An array of many identical slits placed close together with uniform spacing is called a grating.
In a particular grating the slits are narrow enough to diffract the light passing through into a broad wavefront. The waves coming from the many slits interfere, producing bright spots on the screen wherever all these waves arrive in phase.
The slide containing the grating in the laser beam is mounted, the set-up is adjusted to produce a bright red diffraction pattern.
You mark the positions of the central maximum and of three diffraction maxima on either side of it. Then you can measure the distances (x1, x2, x3, x−1, x−2, x−3) of the maxima from the central maximum. What would be reasonable estimates for these values?
Estimate the distance L from the grating to the screen; this will allow you to calculate the diffraction angle θ for each maximum (tan θ n = xn/L).
How would you calculate a value for the wavelength λ of the laser light for each of your ...

Solution Summary

Discussions and calculations about diffraction maximums and estimations for their positions are determined.

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Diffraction of Light: Diffraction Grating

1. A diffraction grating with 2.10E3 slits per centimeter is used to measure the wavelengths emitted by hydrogen gas.
At what angles in the first-order spectrum would you expect to find the two violet lines of wavelengths 434 nm
and 410 nm?
(a) At what angle in the first-order spectrum would you expect to find the first violet line of wavelengths
434 nm?
(b) At what angle in the first-order spectrum would you expect to find the second violet line of
wavelength 410 nm?

2. What is the longest wavelength that can be observed in the fifth-order (m=5) spectrum using a diffraction grating with
3.60E3 slits per centimeter? (Unit: nm)
All answers must have three significant digits unless otherwise specified.

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