Calculate the angle between a refracted wavefront

[Peter G.]

A wave is traveling from medium A to medium B. The ratio: r.i B / r.i A = 1.4. The angle between an incident wavefront and the normal to the boundary is 50 degrees. Calculate the angle between a refracted wavefront and the normal to the boundary:

This is what I did:

n_Asin i = n_B sin r
sin 50 = 1.4 sin r
r = 33.2 degrees

Is that correct?

Thanks,
Peter G.

 

[ehild]

The angle of incidence and the angle of refraction are defined as the angles the direction of propagation encloses with the normal of the surface.
The problem speaks about the angle between the wavefront and the normal of the boundary. The wavefront is a plane, perpendicular to the direction of propagation. How is related this angle to the angle of incidence?

ehild

 

[Peter G.]

Oh, the relation would be 90 - the angle between the normal and the wavefront?

 

[ehild]

Oh, the relation would be 90 - the angle between the normal and the wavefront?

Yes, I think so.

ehild

 

[Peter G.]

So this would mean that my angle of refraction between the wavefront and the normal would therefore be:

nAsin i = nB sin r
sin 40 = 1.4 sin r
90-27.33
=62.67 degrees?

 

[ehild]

The angle between the wavefront and the normal is 62.67 degrees in the refracted wave, but it is not the angle of refraction. The angle of refraction is 27.33°.

ehild

 

[Peter G.]

Ok thanks!