Can someone check my answers to these four wave questions

[question dude]

My textbook didn't include answers to these questions at the back.

Question 1:

my answer:

Question 2:

my answer:

part A and B of the question are shown by wavefronts A and B in the picture below,

Question 3:

my answer:

and just out of curiousity, if the direction of the refracted wave were closer to the direction of the incident waves than the boundary normal, would the gap between the wavefronts be bigger?


Question 4:

my answers:

a) reduced diffraction
b) increased diffraction
c) increased diffraction
d) I'm not sure here. Doesn't this depend on exactly how much the gap is widened by and how long the wavelengths have been increased to?

 

[Redbelly98]

Looks good over all. Some specific comments:

2. I would say you are correct for a rough sketch. A more accurate drawing would show different amounts of curvature for the two waves -- probably not required for full credit/marks here, but that is ultimately up to your instructor.

3. No, the gaps would not be bigger than they are in the incident wave. Think about it: if the refracted wave were in the exact same direction as the incident wave, how would the wavefront gaps compare to those in the incident wave? (I.e., would they be larger, smaller, or the same?)

4-d. You are correct. There is a slight chance that your instructor or the question writer meant the answer to be "no change", but as you said you really can't determine this without knowing the amounts by which the two quantities were changed.

Good job.

 

[question dude]

Looks good over all. Some specific comments:

2. I would say you are correct for a rough sketch. A more accurate drawing would show different amounts of curvature for the two waves -- probably not required for full credit/marks here, but that is ultimately up to your instructor.

can I ask what you mean by that? haven't I done that in the diagram?

3. No, the gaps would not be bigger than they are in the incident wave. Think about it: if the refracted wave were in the exact same direction as the incident wave, how would the wavefront gaps compare to those in the incident wave? (I.e., would they be larger, smaller, or the same?)
.

So for question 3, have I drawn it correctly then? (the gaps would be smaller for the refracted waves)

I assume what you've written here is in reply to my query: ''and just out of curiousity, if the direction of the refracted wave were closer to the direction of the incident waves than the boundary normal, would the gap between the wavefronts be bigger?''

anyway to answer you, if refracted waves were in the same direction as the incident wave, then the wavefront gaps would be the same, right?

You know, I think my query was phrased awkwardly, here's what I want to ask with a diagram to help:

if the refracted direction is the purple arrow (so that wave direction would be further away from the normal than the incident direction), then would the wavefront gaps be bigger?

and also, is it possible for the incident wave to be refracted to the direction of the blue arrow? If it is, how would the gaps between the refracted wavefronts differ from the gaps in the incident waves?

 

[Redbelly98]

can I ask what you mean by that? haven't I done that in the diagram?

In the diagram, the two waves seem to have the same amount of curvature. Probably okay, since they just ask for a sketch, but in reality wave B would be less curved than wave A, having traveled for a longer time.

So for question 3, have I drawn it correctly then? (the gaps would be smaller for the refracted waves)

Yes, sorry I did not clarify that. You did draw it correctly.

I assume what you've written here is in reply to my query: ''and just out of curiousity, if the direction of the refracted wave were closer to the direction of the incident waves than the boundary normal, would the gap between the wavefronts be bigger?''

Yes.

anyway to answer you, if refracted waves were in the same direction as the incident wave, then the wavefront gaps would be the same, right?

Yes.

You know, I think my query was phrased awkwardly, here's what I want to ask with a diagram to help:

if the refracted direction is the purple arrow (so that wave direction would be further away from the normal than the incident direction), then would the wavefront gaps be bigger?

Yes.

and also, is it possible for the incident wave to be refracted to the direction of the blue arrow? If it is, how would the gaps between the refracted wavefronts differ from the gaps in the incident waves?

Nope, it's not possible. The angle θ₂ in your figure must be between 0 and 90^O; it can't become negative and result in the blue ray.

 

[question dude]

In the diagram, the two waves seem to have the same amount of curvature. Probably okay, since they just ask for a sketch, but in reality wave B would be less curved than wave A, having traveled for a longer time.



Yes, sorry I did not clarify that. You did draw it correctly.


Yes.

Yes.

Yes.

Nope, it's not possible. The angle θ₂ in your figure must be between 0 and 90^O; it can't become negative and result in the blue ray.

Thank you so much for the help