Finding the time it takes for light to pass an object

[DODGEVIPER13]

Homework Statement

In the figure below, a light is incident at angle θ1 = 44° on a series of five transparent layers with parallel boundaries. For layers 1 and 3, L1 = 15 µm, L3 = 27 µm, n1 = 1.79, and n3 = 1.48.

(a) At what angle does the light emerge back into air at the right?


°

(b) How long does the light take to travel through layer 3?


ps

Homework Equations

t= LN/C

The Attempt at a Solution

I plugged in L=27e-6 and N =1.48 and C=3e8 but this gave me 1.336e-13 or .1336 ps which is incorrect, what should I do.

 

[Steely Dan]

Remember that the light is not traveling on the shortest path through the thickness of the layer, but rather on a diagonal path because of its refraction through the entry surface. So figure out the actual distance traveled through layer 3 first, and then use that as L in your formula.

 

[DODGEVIPER13]

Man I have tried every thing from putting 27e-6/sin(44) in rads and degrees to the smae thin using cosine and tangent and I am still not getting the right answer. I have also tried (27e-6)sin(44) in rads and degrees same with cosine and tangent. I also did the same in reverse this did not work either what should I do?

 

[Steely Dan]

From the question, it sounds as though it's incident on the first layer from air at the specified angle. But because layer 3 has a different index of refraction than the air, the angle with respect to the normal will be different, in general.