Law of Refraction with changing index of refraction

In summary, the task was to determine the time interval for a light ray to traverse a distance of 101.2-km through the Earth's atmosphere, where the index of refraction increases linearly from 1.00 to 1.000293. An expression was needed for v as a function of altitude, which was found using the equations v1/v2=n2/n1 and v1=3e8. The final step was to write a differential equation using v as dy/dt, which led to the solution for the time interval.
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Mnemonic
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Homework Statement


A light ray enters the atmosphere of the Earth and descends vertically to the surface a distance h = 101.2-km below. The index of refraction where the light enters the atmosphere is n = 1.00 and it increases linearly with distance to a value of n= 1.000293 at the Earth's surface.Over what time interval does the light traverse this path?

Homework Equations


v1/v2=n2/n1

v1=3e8
n1=1
v2=3e8/n2
D=distance from atmosphere barrier

The Attempt at a Solution


So the increase in n2 per m = 1/345392491

Therefore n2=(D/345392491) +1

v2=3e8/(1+(D/345392491))

So v2 changes with distance. I'm not sure where to go from here to get time.
 
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  • #2
See if you can write an expression for v as a function of altitude. That is, if y is the vertical height then v(y) = ?. It will rely on also having an expression for n(y). Then knowing that v is dy/dt you should be able to write a differential equation.
 
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gneill said:
See if you can write an expression for v as a function of altitude. That is, if y is the vertical height then v(y) = ?. It will rely on also having an expression for n(y). Then knowing that v is dy/dt you should be able to write a differential equation.
Thanks I got the answer!
 

FAQ: Law of Refraction with changing index of refraction

1. What is the Law of Refraction?

The Law of Refraction, also known as Snell's Law, describes the relationship between the angle of incidence and the angle of refraction of a light ray passing through a boundary between two different media.

2. How does the index of refraction affect the Law of Refraction?

The index of refraction is a measure of how much a material slows down the speed of light passing through it. As the index of refraction increases, the angle of refraction also increases, resulting in a greater change in direction of the light ray.

3. What happens to the angle of refraction if the index of refraction decreases?

If the index of refraction decreases, the angle of refraction will also decrease. This means that the light ray will bend less as it passes through the boundary between the two media.

4. Can the index of refraction change within a single medium?

Yes, the index of refraction can change within a single medium, such as in a graded index lens. In this case, the light ray will continuously bend as it passes through the medium, rather than at a single boundary.

5. How is the Law of Refraction used in everyday life?

The Law of Refraction is used in a variety of applications, including eyeglasses, camera lenses, and fiber optic cables. It is also the principle behind the formation of rainbows and mirages.

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