How Does Wavefront Orientation Change When Light Enters a Slower Medium?

[Peter G.]

Hi,

A wave is changing from medium A to medium B and it travels slower in medium B than in medium A. If I draw a normal line from the boundary to the wavefront the wavefront in medium B will move away from the normal? I attached to make it more clear

Furthermore, I got this question:

The angle between the wavefronts and the interface in region A is 60. The refractive index _an_b is 1.4.

What I did was: if 60 between wavefront and boundary, 30 degrees between ray and boundary: sin 30 / sin r = 1.4. I then got between the wavefront and the boundary 69.1 degrees but it is wrong, the mark scheme got 38 degrees. Can anyone help me?

Thanks

 

[Doc Al]

It looks like they were specifying the angle with respect to the normal to the surface. (They probably mixed them up.)


Edit: On closer inspection, there's nothing wrong with the diagram or problem statement.

 

[Peter G.]

Um, sorry, I am still a bit confused in relation to how they did it. I attached the question since I didn't word it very clearly in my first post:

 

[Doc Al]

Here's the problem:

What I did was: if 60 between wavefront and boundary, 30 degrees between ray and boundary

What you need in Snell's law is the angle between the ray and the normal.

 

[Peter G.]

Oh, sorry, that was a typo I guess... In the diagram, the angle between the wavefront and the normal is 60 degrees. So I did 90-60 to get the angle between the ray and the normal. I did sin 30 / 1.4 while the mark scheme did sin 60 1.4. So the mark scheme is wrong?

 

[Doc Al]

In the diagram, the angle between the wavefront and the normal is 60 degrees.

No, the diagram is quite clear. The angle between the wavefront and the boundary is 60 degrees.

 

[Peter G.]

Ah, never mind, I got it now. Thanks! But if you wouldn't mind, could you help me with the second part of the question I linked? I got the first part but I am confused as to what the marking scheme says:

position of anyone minimum closer to centre / minima closer together;
frequency increased so wavelength decreased / correct explanation in terms of double-slit equation;

 

[Doc Al]

Ah, never mind, I got it now.

I knew you'd figure it out.

But if you wouldn't mind, could you help me with the second part of the question I linked?

Are you sure you linked it? (See next post--you were still linking when I wrote this.)

 

[Doc Al]

frequency increased so wavelength decreased / correct explanation in terms of double-slit equation;

That's the trick. Do you realize that since the speed of the wave is fixed, increasing the frequency must decrease the wavelength? And how will a smaller wavelength affect the pattern? What does the double-slit equation tell you?

 

[Peter G.]

Sorry Doc Al, I updated the post a few seconds after I posted it. I am tired, I shouldn't be studying until now so I am making those frustrating stupid mistakes But this is the last question and then I am done!

 

[Doc Al]

Look above!

 

[Peter G.]

Ah, the distance between the first destructive interference (half a wavelength) to the center will decrease?

 

[Doc Al]

Ah, the distance between the first destructive interference (half a wavelength) to the center will decrease?

Yes. Smaller wavelength means that a given maximum or minimum will be closer to the center.