Final answer:
The speed of light in water is 2.25 × 108 m/s, and the angle of incidence for light crossing from water to air with a refractive index of 1.33 and an angle of refraction of 67° is 44°, calculated using Snell's law.
Step-by-step explanation:
Refraction and the Speed of Light in Water
When considering refraction, the index of refraction of water, which is 1.33, plays a crucial role in understanding how light behaves as it crosses the boundary between different mediums. When light enters water from air, it slows down; the speed of light in water (c/n) is approximately 2.25 × 108 m/s. Snell's law, n1sinθ1 = n2sinθ2, where n1 and n2 are the indices of refraction of the two media and θ1 and θ2 are the angles of incidence and refraction respectively, allows us to calculate these angles. Given a refractive index of 1.33 and an angle of refraction of 67° when crossing back into air, the angle of incidence within water is found to be 44°.
The relationship between the index of refraction and the speed of light in a given medium is well-established through both theoretical calculations and direct measurements. Therefore, knowing the index of refraction for water enables us to predict and understand the propagation of light through aquatic environments, whether one is considering a laser beam emerging from a submarine or a scuba diver looking at an instructor underwater.