Question

Figure shows wave fronts in still water, moving in the direction of the arrow towards the interface $ PQ $ between a shadow region and a deep (denser) region. Which of the lines shown may represent one of the wave fronts in the deep region?

$ \left( A \right)I \\
  \left( B \right)II \\
  \left( C \right)III \\
  \left( D \right)IV \\ $

Answer 1

Hint :In order to solve the question, we have top head back to the ray optics, and the motion for a ray from the denser to the rarer medium is considered in this case. After that with the knowledge of the wave fronts and the normal and refraction, we draw the actual wave front to be obtained.
The wave front is drawn parallel to the wave motion so the incident wave is drawn and the corresponding wave front as given in the question and then the direction of refracted ray is taken and the perpendicular wave fronts are drawn.

Complete Step By Step Answer:
We know that when a ray of light travels from the rarer to the denser medium, the light ray refracts towards the normal of the interface. Similarly, in this case, the water wave fronts are going from the shallow region to the deep (denser) region. As shown in the figure below, the wave front is perpendicular to the wave motion.

Now if we see the figure given in the question, we observe that the wave front obtained above matches the wave front that is numbered $ I $ in the question.
Hence option $ \left( A \right)I $ is correct.

Note :
The wave front of a time –varying field is the set of all the points where the wave has the same phase of sinusoid. In the refracted wave front in the direction towards the normal. We obtain the ray and the corresponding wave front for it is drawn which is parallel to $ PQ $ only.