How far does light travel underwater during a time interval of \(1.50 \times 10^{-6} \mathrm{s} ?\)

The index of refraction, often denoted by 'n', is a dimensionless number that describes how light propagates through a medium compared to its speed in a vacuum. It's a measure of how much the speed of light is reduced inside the material. For example, water has an index of refraction of about 1.33. This means that light travels 1.33 times slower in water than it does in a vacuum.

Understanding the index of refraction is key to many areas of physics, including optics and wave phenomena. It's crucial when calculating the bending of light as it enters different media, known as refraction. The higher the index, the more the light bends, as it slows down. This concept helps explain phenomena such as the apparent bending of a straw in a glass of water or why pools look shallower than they are.

The speed of light in a vacuum, represented as 'c', is a fundamental constant of nature that plays a pivotal role in the theory of relativity and our understanding of space and time. This speed is exactly 299,792,458 meters per second. Light's speed in a vacuum is the ultimate speed limit, meaning nothing in the universe can travel faster.

In physics problems, when we refer to the speed of light, it usually means this constant speed in a vacuum. It's interesting to note that the speed of light isn't just important for light itself but also for other electromagnetic radiation, such as radio waves, microwaves, and gamma rays, which all travel at this same maximum speed in a vacuum.

Distance calculation is a fundamental concept in physics, essential for solving many types of problems. The basic formula to calculate the distance ('d') traveled by an object when its speed ('v') and travel time ('t') are known is:\[d = v \times t\]This formula assumes that speed is constant over the time traveled, making it straightforward to apply to problems involving the speed of light since light travels at a constant speed through a homogeneous medium. Calculations of distance can become more complex when dealing with accelerating objects or when the speed varies over time, but for light traveling underwater or in any other uniform medium, the calculation remains relatively simple as it follows the constant speed.

Physics problem solving is not just about plugging numbers into formulas; it's about understanding concepts and their interrelations. Effective problem-solving often involves several steps, from identifying known and unknown quantities to choosing the relevant equations and finally computing the values. It's important to thoroughly understand the problem at hand and visualize the physical scenario. Approaching problems step-by-step as shown in the exercise: finding the speed of light underwater and then calculating the distance it travels, helps to break down complex problems into manageable parts.

Another key aspect of problem-solving in physics is making assumptions when necessary and estimating to simplify the problem without significantly affecting the accuracy of the results. It includes using appropriate significant figures and units, ensuring the final answer is both accurate and practical.