67. (a) The ﬁrst contribution to the overall deviation is at the ﬁrst refraction:
δθ
1
=
θ
i
−
θ
r
. The next
contribution to the overall deviation is the reﬂection. Noting that the angle between the ray right
before reﬂection and the axis normal to the back surface of the sphere is equal to
θ
r
, and recalling
the law of reﬂection, we conclude that the angle by which the ray turns (comparing the direction
of propagation before and after the reﬂection) is
2
= 180
◦
−
2
θ
r
. The ﬁnal contribution is the
refraction suFered by the ray upon leaving the sphere:
3
=
θ
i
−
θ
r
again. Therefore,
θ
dev
=
1
+
2
+
3
= 180
◦
+2
θ
i
−
4
θ
r
.
(b) We substitute
θ
r
= sin
−
1
(
1
n
sin
θ
i
) into the expression derived in part (a), using the two given values
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics

Click to edit the document details