Question
A light ray enters the atmosphere of a planet and descends vertically to the surface a distance $h$. The index of refraction where the light enters the atmosphere is $1.000$, and it increases linearly to the surface where it has a value of $n$. (a) How long does it take the ray to traverse this path? (b) Compare this to the time it takes in the absence of an atmosphere.
Step 1
At the surface of the planet, the distance is $h$ and the index of refraction is $n$. Therefore, we can write the index of refraction as a linear function of $x$: \[n(x) = 1 + \frac{n - 1}{h}x\] Show more…
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