Optical Path Length: Calculate w/ Refractive Index & Length

[istinkatphysics]

This is the question:
The optical path length of a light beam is nd where n is the refractive index and d is the physical distance. A light beam passes through 2.0 in thick glass (n=1.525) and then through 12 in. of water (n=1.33) and finally though 0.6 in of polystyrene (n=1.590). What is the optical path length?

Is this too easy to just multiply the refractive index by the length and then add all of those numbers? When I did that I got about 20 inches. I was also wondering if I missed a trick or anything in this problem. The length could be different (instead of using the values of 2 in, 12 in, and 0.6 in) because the light becomes bent (with the refractive index). Does this set up a triangle in the glass, water, and polystrene? Is only the one side of the triangle 2 in and i am looking for the hypotenuse as a length value? If so how would i calculate that with no angles (or only a 90 degree one)?
Thanks for reading.

 

[Twigg]

Is this too easy to just multiply the refractive index by the length and then add all of those numbers?

This is correct. I also get about 20.

I was also wondering if I missed a trick or anything in this problem.

Nope!

The length could be different (instead of using the values of 2 in, 12 in, and 0.6 in) because the light becomes bent (with the refractive index).

The light only refracts if it's incident at an angle to the interface. Since they don't give you an incident angle, it's safe to assume that the light is initially perpendicular to each interface and all the interfaces are parallel to each other.