Calculating Refraction Time in Water: Physics Homework Help

[eestep]

Homework Statement

Light is originally traveling through air and then enters water with an index of refraction of 1.32. Angle in air at interface is 69 degrees with respect to normal. If thickness of water is 2.3 km, how long does it take in microseconds (1 x 10^-6 s) to cross water? Hint: light does not travel straight across water because it is refracted by water. Answer is 15.34.

Homework Equations

n_asin$$\phi$$_a=n_bsin$$\phi$$_b
n=c/v

The Attempt at a Solution

(1)sin69=1.32sin$$\phi$$_b
$$\phi$$_b=sin^-1(sin69/1.32)=45.01
cos$$\phi$$_b=d/h
h=d/cos$$\phi$$_b
nv=c
v=h/t=c/n
t=hn/c=dn/ccos$$\phi$$_b x 10⁶=(2.3 x 10³m*1.32)/(3 x 10⁸cos45.01) x 10⁶=14.31
I am not certain what I am doing wrong, but that answer is incorrect.

 

[ehild]

It looks correct.

ehild