Solving Diffraction Grating Homework: Max Wavelength at 11°

AI Thread Summary
A monochromatic plane wave is incident on a diffraction grating with 105 lines/m, and the goal is to find the visible wavelengths that produce a maximum at 11°. The relevant equation is d*sinθ = m*λ, where d is the grating spacing. The spacing is calculated as d = 1 x 10^-5 m, and it is noted that m can be any whole number. The solutions found indicate that for m = 3 and m = 4, the visible wavelengths are 636 nm and 477 nm, respectively. This demonstrates how to apply the diffraction grating formula to determine specific wavelengths.
Swan
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Homework Statement


A monochromatic plane wave is normally incident on a diffraction grating with 105 lines/m. For what visible wavelengths would this grating produce a maximum at 11°.

Homework Equations


d*sinθ = m*λ


The Attempt at a Solution


d = 1 x 10-5 m

I don't get how to actually solve it because i don't know what the m for this situation would be.
 
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Hi Swan! :smile:
Swan said:
For what visible wavelengths would this grating produce a maximum at 11°.
…
I don't get how to actually solve it because i don't know what the m for this situation would be.

(we usually use "n", not "m")

it can be any whole number …

there may be more than one value for which there is a solution :wink:
 
tiny-tim said:
Hi Swan! :smile:


(we usually use "n", not "m")

it can be any whole number …

there may be more than one value for which there is a solution :wink:

Hello tiny-tim. Thank You for replying. How would i go about solving this question?
 
by using your equation …

what do you get? :smile:​
 
tiny-tim said:
by using your equation …

what do you get? :smile:​

I got at m = 3 and m = 4 the diffraction grating would produce a maximum at 11° at visible wavelengths of 636 nm, 477 nm respectively to m = 3, m = 4.
 
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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