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.
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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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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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