Wavelength directly affects the angle at which light is diffracted by a diffraction grating: shorter wavelengths are diffracted at smaller angles, while longer wavelengths are diffracted at larger angles. This difference in diffraction angles for different wavelengths is what allows a diffraction grating to separate white light into its constituent colors.
Here's a more detailed explanation:
The Grating Equation
The behavior of a diffraction grating is governed by the grating equation:
d sin θ = mλ
Where:
- d is the spacing between the grating lines (the distance between adjacent slits).
- θ is the angle of diffraction (the angle between the diffracted beam and the normal to the grating).
- m is the order of diffraction (an integer representing the different diffracted beams; m = 0, ±1, ±2, ...).
- λ is the wavelength of the light.
Impact of Wavelength on Diffraction Angle
From the grating equation, we can see that for a given diffraction grating (constant d) and a specific order (m), the angle of diffraction (θ) is directly related to the wavelength (λ). Specifically:
sin θ = mλ / d
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Longer Wavelengths (Larger λ): A larger wavelength means a larger value for sin θ. Consequently, θ, the angle of diffraction, will be larger. Red light, having a longer wavelength, will be diffracted at a larger angle than blue light.
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Shorter Wavelengths (Smaller λ): A shorter wavelength means a smaller value for sin θ. The angle of diffraction (θ) will be smaller. Blue or violet light will be diffracted at smaller angles compared to red light.
Practical Implications and Examples
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Separation of White Light: When white light (which contains a mixture of all visible wavelengths) shines on a diffraction grating, each wavelength is diffracted at a different angle. This is how a diffraction grating separates white light into its spectrum of colors, similar to a prism.
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Spectroscopy: Diffraction gratings are a crucial component of spectrometers, which are used to analyze the spectral composition of light. By measuring the angles at which different wavelengths are diffracted, scientists can identify the elements present in a sample and study their properties.
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Holography: Diffraction gratings play a role in creating and viewing holograms.
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CDs and DVDs: The surface of a CD or DVD acts as a diffraction grating, producing the rainbow-like patterns you see when light reflects off it.
Summary Table
| Wavelength | Diffraction Angle (θ) |
|---|---|
| Longer (e.g., Red) | Larger |
| Shorter (e.g., Blue) | Smaller |
In conclusion, the wavelength of light significantly influences how it is diffracted by a diffraction grating. Longer wavelengths are diffracted at larger angles, and shorter wavelengths are diffracted at smaller angles, allowing diffraction gratings to separate light into its component colors.
