Ranking materials in order of their refraction index.

AI Thread Summary
The discussion focuses on ranking materials based on their refractive indices, with a specific emphasis on understanding the relationship between angles of incidence and refraction. The initial analysis concludes that nC is greater than nA and nB, leading to the ranking nC > nA > nB. However, the correct ranking is nA > nC > nB, prompting confusion about why nA is greater than nC despite the observed angles. The key point of contention revolves around the interpretation of angles relative to the normal, which affects the refractive index calculations. Clarification on this concept is sought to resolve the discrepancy in rankings.
vf_one
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Hi everyone

I'm having a bit of trouble solving this question. If anyone can help that would be awesome

Homework Statement
Rank the materials in the diagram according to their refractive indices from greatest to smallest (see attachment)

The attempt at a solution
The greater the refractive index of a material, the slower the wave will travel and therefore the more it will bend towards the normal.

From the diagram, the angle of refraction in medium C is smaller than the angle of incidence in medium A so nC > nA

The angle of incidence in medium C is smaller than the angle of refraction in medium B so nC > nB

the wave seems to travel a lot faster in medium B than A as it bends further away from the normal so nA>nB

So nC > nA > nB

But the answer is nA > nC > nB

Why is nA > nC??
 

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  • refractive index.jpg
    refractive index.jpg
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Both the angle of incidence and the angle of refraction are measured from the normal of the surface.

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

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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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