67. (a) The ﬁrst contribution to the overall deviation is at the ﬁrst refraction:δθ1=θi−θr. The nextcontribution to the overall deviation is the reﬂection. Noting that the angle between the ray rightbefore reﬂection and the axis normal to the back surface of the sphere is equal toθr, and recallingthe law of reﬂection, we conclude that the angle by which the ray turns (comparing the directionof propagation before and after the reﬂection) is2= 180◦−2θr. The ﬁnal contribution is therefraction suFered by the ray upon leaving the sphere:3=θi−θragain. Therefore,θdev=1+2+3= 180◦+2θi−4θr.(b) We substituteθr= sin−1(1nsinθi) into the expression derived in part (a), using the two given values
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.