An acrylic block similar to that used in our lab is surrounded by water. The ind

Question

An acrylic block similar to that used in our lab is surrounded by water. The index of refraction of the acrylic is 1.50; the index of refraction of the water is 133. (a) Is total internal reflection possible for light passing from this acrylic to water? If so, calculate the critical angle for total internal reflection. If not, clearly show why not. (b) Is total internal reflection possible for light passing form water to this acrylic? If so, calculate the critical angle for total internal reflection. If not, clearly show why not. For the rest of the problem, consider light that has already entered the acrylic, as shown. A ray in the acrylic approaches surface A at an angle of incidence of 18. 7 degree. Some light is refracted into the water the rest is reflected. (c) Calculate the angle of refraction for the ray exiting the acrylic block at surface A. (d) Calculate the angle of incidence for the ray approaching surface B.

Explanation / Answer

(a) Total Internal Refraction (TIR) is only possible when light approaches from a denser medium to a less dense medium.So TIR is possible when light comes fom a denser medium Acrylic,with a Refractive Index of 1.5 (n1) to a less dense medium water which has a Refrative Index of 1.33 (n2).

We know Snell's Law states that n1 sin (incedent angle) = n2 sin (Refracted angle)

In order that TIR takes place, Refracted angle must be at lease 90 degrees. since sin 90 =1, we get

So 1.5 sin (Incident Angle) = 1.33 x 1

This gives sin (incident angle) = 1.33/1.5 = 0.8866.

Which gives incident angle = sin -1 (0.8866) = 62.44 degrees. This is known as the Critical Angle. Answer

(b) TIR is not possible when light comes from a lighter medium like water (1.33) to a denser medium like Acrylic. Hence there is no question of a Critical Angle. A moment of thinking would make it more clear. Light refracts away from the normal at the point of incidence when light travels from a denser to a rarer medium. So angle of refraction becomes 90 degree first before the angle of incidence becomes 90 degree. For TIR, angle of refraction must be at least 90 degrees. This can not happen when light travels towards the normal when travelling from a lighter to a denser medium. So TIR can not happen when light travels from water to acrylic. Answer

(c) Applying Snell's Law again we get 1.50 sin 18.7 = 1.33 sin (Angle of refraction)

Or 1,50 x 0.32 = 1.33 x sin (Angle of refraction)

solving, Angle of refraction = 21.15 degrees Answer

(d) Angle of reflection = angle of incidence = 18.7 degree Answer.

  

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