Part A First, let's look at a plane wave that is incident on a flat piece of material with an index of refraction .

Part A(Part A 3 figure) .Express your answer in terms of the variables , , and the speed of light in a vacuum .=CorrectNote that there would be no change in the direction of the wavefront at any point because the waverfront encountered the material interface at the same time at all points. Thus all of the individual wavefronts all propagated at the same speed, thereby maintaining the flat wavefront.Now, instead of having a flat wavefront propagating normal to the material interface we have a flat wavefront propagating toward the material at an angle of relative to the axis perpendicular to the material interface. In this part, we will look at the relative positions of a few points--A, B, and C--on the wavefront to illustrate Huygens' principle. (Intro 1 figure) Point C touches the vacuum/material interface at time whereas point B is a distance and point A is a distance away from the interface.Part BWhat is the time it will take for point B of the wavefront to encounter the vacuum/material interface?Express your answer numerically to two decimal places in units of (the time it takes light to travel a distance in a vacuum).CorrectIt should be noted that the accuracy of the method increases the smaller the distance is before making a new wavefront and redoing the wavelets. If you tried to just draw a large wavelet from point B then it would hit the surface after only traveling a distance . This large wavelet would make it difficult to visualize how to add up all of the other wavelets to make a coherent wavefront. As a result, one should just draw a line perpendicular to the wavefront at point B until it hits the surface, at which point the wavelets will change owing to the new index of refraction.Part CHow far did point C go into the material interface in the time that it took for point B to get to the interface? For this part we are looking for the distance traversed by the point C in the material ( ).Give your answer in terms of the time , , and .=CorrectPart DWhat is the new angle at which point C of the wavefront is propagating (relative to a line perpendicular to the vacuum/material interface)? Try to use the fact that you have a spherical wavefront propagating from at the point where C met the vacuum/material interface until time when the wavefront at point B reached the interface.Express your answer in terms of inverse trig functions and .