What is the greatest number of lines per centimeter a diffraction grating can have and produce a complete second-order spectrum for visible light?
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What is the greatest number of lines per centimeter a diffraction grating can have and produce a complete second-order spectrum for visible light?
The wavelength of visible light ranges from 400 nm to 700 nm.
For diffraction:
where,
is the order of diffraction,
is the wavelength of the incident light,
is the distance between the two slits, and
is the angle of diffraction.
The maximum wavelength for visible light is 700 nm. The least separation should diffract at least the maximum wavelength of visible light. So the minimum slit separation that produces a complete second-order spectrum can be calculated as:
Since we want the minimum , should be maximum i.e. 1:
The minimum number of lines per centimeter is inverse of the minimum slip separation:
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