71) A ray of light is incident in air on a block of transparent solid whose inde

Question

71) A ray of light is incident in air on a block of transparent solid whose index of refraction is n. If n = 1.38, what is the largest angle of incidence, ?a, for which total internal reflection will occur at the vertical face (point A shown in the Figure)?

air on a block of ndex of refraction e largest angle of tal internal reflec- ical face (point A n air on a block of 80. Il Optical a DATA portant mol traverses a plane of po ization cloc The amoun path of the through two 40 parallel to the axis be. When the tube A the light 8.72 ns to , but when the tube t jelly, it takes the FIGURE 23.60 vel its length. What Problem 71. his jelly? leuc :0

Explanation / Answer

At a small angle of incidence in air, the internal angle of incidence (on a vertical side) is large .. greater than the critical angle for TIR (the ray totally internally reflects)

Increasing the angle in air reduces the internal angle of incidence .. until this internal angle reaches the critical angle (C) - any further reduction prevents TIR occurring.

When the internal angle of incidence is C, the refracted angle from air (r) = (90 - C)
Sin C = 1/1.38 .. .. C = 46.4º .. .. .. and r = 43.4º

For the ray in air .. n = sin i(max) / sin r
Sin i(max) = n.sin r .. .. 1.38 x sin43.4 = 0.9481 .. .. .. i (max) = 71.46º

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