How long does it take the ray to traverse this path?

[mba444]

Homework Statement

A light ray enters the atmosphere of a
planet where it descends to the surface
15.2 km below. The index of refraction where
the light enters the atmosphere is 1.2 and it
increases uniformly to the surface where it has
a value of 1.55.
I) How long does it take the ray to traverse this path? Answer in units of s.
II) How long would it take to cover the same distance in a vacuum? Answer in units of s.

Homework Equations

speed of light= 2.99*10^8
delta V = C/(delta N)
delta V= delta X / delta t

The Attempt at a Solution

For Question I what i did is that
delta N = N2-N1= 1.55-1.2= 0.35
delta V = (2.99*10^8)/(0.35) = 8.54*10^8 m/s
delta t = 15.2*10^3/8.54*10^8= 1.779*10^-5sec

but I am not sure if my way is correct can someone please check and tell me if I am going wrong somewhere

and for II) i didnt understand what is needed therefore i didnt know how to attempt at a solution



need your help and thanks in advance

 

[rl.bhat]

V1 = C/N1
V2 = C/N2
delta V = C( 1/N1 - 1/N2)

 

[mba444]

i didnt understand

 

[rl.bhat]

Velocity in the medium = velocity of light in vacuum/refractive index of the medium.
So Δv = C/N1 - C/N2

 

[merryjman]

is this a calculus-based course? because i think you would need to use calculus in a situation where the refractive index changes uniformly. as for the second part, it's much easier than you're making it. after all, the index of refraction is relative to the vacuum. for instance, in a piece of glass with index n=1.5, light travels 1.5 times more quickly in a vacuum than it does in the glass.