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Unformatted text preview: 65. Since the layers are parallel, the angle of refraction regarding the ﬁrst surface is the same as the angle
of incidence regarding the second surface (as is suggested by the notation in Fig. 3455). We recall that
as part of the derivation of Eq. 3449 (Brewster’s angle), the textbook shows that the refracted angle is
the complement of the incident angle:
θ2 = (θ1 )c = 90◦ − θ1 .
We apply Eq. 3449 to both refractions, setting up a product:
n2
n1 n3
n2
n3
n1 = (tan θB 1→2 ) (tan θB 2→3 ) = (tan θ1 ) (tan θ2 ) . Now, since θ2 is the complement of θ1 we have
tan θ2 = tan(θ1 )c = 1
.
tan θ1 Therefore, the product of tangents cancel and we obtain n3 /n1 = 1. Consequently, the third medium is
air: n3 = 1.0. ...
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 Fall '08
 SPRUNGER
 Physics

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