The drawing shows a ray of light traveling from point A to point B , a distance

Question

The drawing shows a ray of light traveling from point A to point B, a distance of 4.54 m in a material that has an index of refraction n1. At point B, the light encounters a different substance whose index of refraction is n2 = 1.63. The light strikes the interface at the critical angle of ?c = 48.4

The drawing shows a ray of light traveling from point A to point B, a distance of 4.54 m in a material that has an index of refraction n1. At point B, the light encounters a different substance whose index of refraction is n2 = 1 63. The light strikes the interface at the critical angle of theta C = 48.4degree. How much time docs it take for the light to travel from A to B?

Explanation / Answer

Required time, t = 4.54/v, where v = velocity of light in the medium with refractive index n1. We also have
n1/1.63 = 1/sin 48.4 or n1 = 1.63/(sin 48.4) = 2.17 and so v = (3.0*10^8)/2.17 = 1.38*10^8 m/s
So t = 4.54/[1.38*10^8] = 3.2*10^-8 s = 32 ns

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