Refraction of wavefront in water

[Jahnavi]

Homework Statement

Homework Equations

The Attempt at a Solution

I think the water waves will undergo refraction from the interface and since it is denser , it should bend towards the normal .

By that logic 4) should be correct , but this is incorrect .

I might be applying wrong concept in this problem .

 

[TSny]

You will need to know how the wave speed in deep water compares to the wave speed in shallow water. Deeper is not analogous to denser.

 

[Jahnavi]

Deeper is not analogous to denser.

This is mentioned in the problem statement .

 

[TSny]

This is mentioned in the problem statement .

Yes. That seems strange to me. Anyway, the answer will depend on whether water waves speed up or slow down when passing from shallow to deep. A web search should provide the answer.

 

[Jahnavi]

Anyway, the answer will depend on whether water waves speed up or slow down when passing from shallow to deep.

Water waves will speed up , which means the deeper region acts as rarer medium for waves . Waves should bend away from normal .

 

[Jahnavi]

But then which one bends away from normal ?

 

[TSny]

I like to think in terms of rays rather than wavefronts when considering "bending toward the normal" or "away from the normal". So, I find it helpful to draw some rays as well as wavefronts.

If the waves travel faster in the deep water, then do the rays bend toward or away from the normal when crossing the interface?

(I'm not feeling confident about this problem due to the reference to "denser".)

 

[Jahnavi]

By the way arrow in the picture represents a ray ?

If the waves travel faster in the deep water, then do the rays bend toward or away from the normal when crossing the interface?

Away from normal .

And since wavefront would be perpendicular to refracted ray , option 2) looks a possible option as the refracted wavefront .

Is that correct ?

 

[TSny]

By the way arrow in the picture represents a ray ?

Yes

Away from normal .

Yes

And since wavefront would be perpendicular to refracted ray , option 2) looks a possible option as the refracted wavefront .

How would the direction of a ray for wavefront II compare to the direction of the ray in the shallow region?

I hope I'm not misleading you regarding the change in wave speed. The speed of waves in very deep water depends on the frequency of the waves while the speed of waves in very shallow water depends on the depth of the water and not the frequency. For intermediate depths the speed depends on both the frequency and depth. So, I'm not sure it's generally true that waves speed up when suddenly going from a shallow region to a deep region. I was thinking of the explanation that some people give for why ocean waves "break" when approaching the beach. They claim it's due to the waves slowing down as they move into the shallow region. Maybe the problem is intending you to use the reference to "denser" as indicating that the waves actually slow down in going to the deeper region. Hopefully, others will provide some guidance.

 

[Jahnavi]

Maybe the problem is intending you to use the reference to "denser" as indicating that the waves actually slow down in going to the deeper region.

Assuming this , the refracted ray bends towards the normal .The wavefront which is perpendicular to this refracted ray is I) which is actually the given answer

If you assume for the time being that deeper is denser , then would you agree that refracted ray bends towards the normal and refracted wavefront would be I ) ?

 

[TSny]

Assuming this , the refracted ray bends towards the normal .The wavefront which is perpendicular to this refracted ray is I) which is actually the given answer

If you assume for the time being that deeper is denser , then would you agree that refracted ray bends towards the normal and refracted wavefront would be I ) ?

Yes!

 

[Jahnavi]

Thanks !