Is the Book Wrong About Total Internal Reflection and Snell's Law?

AI Thread Summary
The discussion centers on the relationship between angles of incidence and refraction as described by Snell's Law. The book is affirmed to be correct, stating that as the angle of incidence increases, the angle of refraction also increases, particularly when comparing different indices of refraction. A key point is that the frequency of light remains constant when transitioning between media, while the speed and wavelength change to maintain the relationship between them. Participants suggest visualizing wave fronts to understand how frequency and wavelength interact in different media. Overall, clarity on these principles is essential for grasping the concepts of refraction and wave behavior.
AznBoi
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As the angle of incidence increases, the angle of refraction becomes larger.

Should the underlined word be decreases? why? I think I've found a mistake in the book because according to snell's law of refraction n1sin(theta)1=n2 sin(theta)2 right? If n1>n2 then (theta)1<(theta)2

Wait, I don't know now. I think I'm getting mixed up with angles and indices. =[ Help please.
 
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Is there any easy way to remember the relation of n=c/v, snails law, and how the refracted angle behaves when n1>n2 or vice versa?
 
Also, how come the frequency of light doesn't change as is passes from one medium to another? How do you know if the speed of the wave, frequency, or wavelength changes? I know that the speed of sound/light changes when it goes through another medium but how do you know if frequency or wavelength change or stays constant? Is there a rule for this concept? Thanks
 
bump. help anyone please?
 
AznBoi said:
As the angle of incidence increases, the angle of refraction becomes larger.

Should the underlined word be decreases? why? I think I've found a mistake in the book because according to snell's law of refraction n1sin(theta)1=n2 sin(theta)2 right? If n1>n2 then (theta)1<(theta)2

Wait, I don't know now. I think I'm getting mixed up with angles and indices. =[ Help please.


The book is correct. The angle of the refracted ray will bend away from the normal for increasing values of incident angle, in both cases of n1>n2 and n1<n2. Perhaps work out a table of values to see for yourself.
 
I will try to explain this, as I learned it. Maybe someone can fill it in a bit.
If you think of the wave fronts being parallel to the boundary between the two media, the number of wave fronts (so frequency) passing a point in medium 1 must be the same as the number of wave fronts passing a point in medium 2. If this were not true, wave fronts would be piling up or being destroyed or whatever and there is no physical mechanism for that to happen. So since the speed changes, the wavelength must change, to keep the relation of velocity = frequency*wavelength valid (in both media).

Hopefully that helps a bit.
 
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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