When light travels through a different medium, several phenomena can occur, but the most relevant points from your options are:
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Light waves refract when they travel through a different medium. - This is the correct statement. Refraction is the bending of light as it passes from one medium to another due to a change in its speed. The degree of bending depends on the refractive indices of the two media.
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Light waves reflect when they travel through a different medium. - This can also happen, but it is not guaranteed. Reflection occurs when light encounters a boundary between two different media, and some of the light is reflected back into the original medium while some may be refracted.
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Light waves always stop moving when they hit a different medium. - This statement is incorrect. Light does not stop moving when it enters a different medium; it continues to travel at a different speed dependent on the optical properties of the medium.
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Light waves speed up when they travel through a different medium. - This is only partially true. Light speeds up when it moves from a medium with a higher refractive index to one with a lower refractive index (e.g., from water to air). Conversely, it slows down when moving into a medium with a higher refractive index (e.g., from air to glass).
In summary, the most accurate and comprehensive statement regarding light traveling through different media is that light waves refract when they do so.