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... show more 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.
2 answers 2