Two beams of light start together and then hit a slab of two

Two beams of light start together and then hit a slab of two different kinds of material. This will cause one of the beams to get \"ahead\" of the other; that is, one will emerge from the slab sooner than the other. The beams have a wavelength of 430 nm outside the slabs, and the slab is d = 1.30 microns thick. If the top half of the slab has index of refraction 1.71 and the bottom has index 1.34, by what time interval will one of the beams be ahead of the other once they\'ve gone through the slab?

Solution

We know that the speed with which a ray travels in a medium of refractive index is given as:

C1 = C / where is the refractive index of the particular medium and C is the speed of the ray in vacuum.

Now for the above case we will determine the speed of the two rays while travelling through the respective media and then determine the time lag that would come in them after travelling through the thickness of d = 1.3 micron.

Speed of the top ray = C1 = C / 1.71

Speed of bottom ray = C2 = C / 1.34

Time lag = D[1 / C1 - 1/C2] = 1.3 x 10^-6 [1.71 - 1.34] / C = / 2.99792458 x 10⁸

That is, time lag = 0.160 x 10^-14 seconds