Final answer:
The echo heard by students in a cave is caused by the reflection of sound waves, while objects looking distorted in water is due to the refraction of light waves. The index of refraction of a medium where light speed is measured as 1.3×10^8 m/s is calculated to be approximately 2.31.
Step-by-step explanation:
Exploring Echoes and Light in Different Mediums
During a cave exploration, students noticed that they heard an echo when they spoke. This is most likely caused by the reflection of sound waves. When the sound waves collide with the cave walls, they are reflected back, allowing the students to hear an echo of what they have said. The other phenomenon associated with waves is diffraction. This occurs when waves bend around obstacles, such as water waves bending around a boat, or sound spreading out after passing through a doorway.
For the second part of the student’s question, objects appearing different in size and shape in a container of water is caused by the refraction of light waves. When light passes from air into water, the change in speed causes the light to change direction, making objects appear different than they would in air.
As for determining the index of refraction of a medium when a physicist measures the speed of an electromagnetic wave at 1.3×108 m/s, the index of refraction (n) can be calculated using the formula n = c/v, where c is the speed of light in a vacuum (approximately 3×108 m/s) and v is the speed of light in the medium. Therefore, if a wave travels at 1.3×108 m/s in a medium, while the speed of light in a vacuum is 3.0×108 m/s, the index of refraction for that medium would be about 2.31.