Calculate speed when light in a vacuum is 300,000 km/s. If the index of refraction of water is 1.33, what is the speed of light in the water?

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Q: 

Assume the speed of light in a vacuum to be 300,000 km/s. Assuming the index of refraction of water to be 1.33, what is the speed of light as it passes through a medium of water? 

A:

This is a case of refraction of light as it enters a medium. In the process of refraction, light is bent or curved as it passes from one medium into another. The index of refraction allows us to quantify this change in light's velocity. Although light technically moves ever so slightly slower in air, we can consider the speed of light through air to be essentially equal to the speed of light within a vacuum. 

The following formula defines the index of refraction:

`n = c/v`

Here, `n` is the index of refraction (a ratio which has no units), `c` is the speed of light in a vacuum, which for our purposes is `300,000 (km)/s`, and `v` is the velocity of light as it passes through the medium in question (in this case, water).  

Therefore, we will solve for `v` in the above equation.

Plugging in the known values from the question, we now have the following:

`1.33 = (300,000 (km)/(s))/v`

After multiplying both sides of this equation by `v`, we obtain the following:

`1.33*v = 300,000 (km)/(s)`

We can now divide the right side by 1.33 to obtain the value of `v`.This gives us `225,563.9098 (km)/(s)` , which if rounded to three significant digits will be`226,000 (km)/s` . This is our final answer. This makes sense as an answer because light will be slowed down as it enters water. 

 

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