# Physics Geometric Optics question?

Question:
A light ray enters the atmosphere of a large planet and descends vertically to the surface a distance h = 1.00X10^5 km below. The index of refraction where the light enters the atmosphere is, of course, 1.000. As the light descends into the atmosphere the index of refraction n(x) increases linearly with...
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Question:

A light ray enters the atmosphere of a large planet and descends vertically to the surface a distance h = 1.00X10^5 km below. The index of refraction where the light enters the atmosphere is, of course, 1.000. As the light descends into the atmosphere the index of refraction n(x) increases linearly with distance x below the top of the atmosphere, reaching the value n(h) = n0 = 1.50 at the surface of the planet (where x = h).

(a) How long after the light enters the atmosphere (t=0) does it reach the surface of the planet?

(b) How does your value for t compare with the time interval required in the absence of an atmosphere?

I tried solving part (a) and got up to n(x) = (5.00X10^-6)x + 1.0...

Need to solve for time it took but kinda stuck from there.

A light ray enters the atmosphere of a large planet and descends vertically to the surface a distance h = 1.00X10^5 km below. The index of refraction where the light enters the atmosphere is, of course, 1.000. As the light descends into the atmosphere the index of refraction n(x) increases linearly with distance x below the top of the atmosphere, reaching the value n(h) = n0 = 1.50 at the surface of the planet (where x = h).

(a) How long after the light enters the atmosphere (t=0) does it reach the surface of the planet?

(b) How does your value for t compare with the time interval required in the absence of an atmosphere?

I tried solving part (a) and got up to n(x) = (5.00X10^-6)x + 1.0...

Need to solve for time it took but kinda stuck from there.

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