What is the correct way to separate light into its component colors?

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Light can be separated into its component colors primarily through diffraction gratings and thin film interference. While focusing a broad beam of light intensifies it, it does not separate colors like a prism does. Diffraction gratings work by utilizing a periodic structure to split and diffract light into multiple beams, with their directions influenced by the grating's spacing and the light's wavelength. This explains why the correct answer is both a and b, rather than just focusing the light. Understanding these optical principles is essential for accurately interpreting how light dispersion occurs.
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Homework Statement


1. Light can be separated into its component colors by:

a. diffraction gratings

b. thin film interference

c. focusing a broad beam of light into a point

d. bends light as it passes the edge of an object

*e. both a and b

The Attempt at a Solution



I thought the answer was c because it seems like what happens in a prism, but apparently (answer key) its e. Can someone explain why? Thanks!
 
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C, focusing a broad beam of light into a point is simply intensifying the light, kind of like using a magnifying glass to burn something. A prism slows down the wavelengths just enough so that the different wavelengths separate.
 


ok but why do diffraction gratings separate the colors?
 


http://en.wikipedia.org/wiki/Diffraction_grating

From the article above: "In optics, a diffraction grating is an optical component with a periodic structure, which splits and diffracts light into several beams traveling in different directions. The directions of these beams depend on the spacing of the grating and the wavelength of the light so that the grating acts as the dispersive element."
 
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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