Grating, second-order spectrum and interference

AI Thread Summary
To prevent a second-order spectrum for any visible wavelength between 400 nm and 570 nm, the grating must have a specific minimum number of lines per centimeter. The equation dsin(theta) = m(lambda) is crucial for determining this, where d is the grating spacing, m is the order of the spectrum, and lambda is the wavelength. A diagram illustrating the positions of the first-order blue and red spectra, along with the edge of the second-order spectrum, can aid in visualizing the problem. The discussion revolves around calculating the necessary grating density to ensure that the second-order spectrum does not appear. Understanding these principles is essential for solving the homework problem effectively.
erinec
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Homework Statement


What is the minimum number of lines per centimeter that a grating must have if there is to be no second-order spectrum for any visible wavelength? (Let visible region extend from 400 nm to 570 nm.) Hint: Draw a diagram showing the relative positions of the rays corresponding to the first-order blue spectrum, the first order red spectrum, and the edge of the second-order spectrum.


Homework Equations


dsin(theta) = m(lambda)


The Attempt at a Solution


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