Path of Light in Time-Varying Refractive Index: Straight or Curved?

AI Thread Summary
The discussion centers on the path of light in a liquid with a time-varying refractive index. Participants debate whether the light will travel in a straight line or curve. One contributor argues that the light will follow a straight path due to the nature of time variation. Another agrees, noting that symmetry implies no directional bias in the curvature. The consensus leans towards the belief that light will not curve under these conditions.
arpon
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Homework Statement


Suppose, light is passing through a liquid whose refractive index is time-varying. What will be the path of light ray ? Will it be a straaight line or curve ?

Homework Equations

The Attempt at a Solution


I think, it will be a straight line.
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arpon said:
time-varying
Are you certain the problem statement specified "time varying" and not a spatial variation such as refractive index of atmosphere with altitude?
 
Bystander said:
Are you certain the problem statement specified "time varying" and not a spatial variation such as refractive index of atmosphere with altitude?
No spatial variation.
 
arpon said:
I think, it will be a straight line.
I agree with your reasoning. By symmetry, there is no reason it should start curving one way rather than the other.
 
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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