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consider the situation shown in figure

July 26, 2018 0

solution:
consider the figure 
l e t space mu subscript 2 equals 1.0 mu subscript 1 equals 1.25 theta to the power of " equals sin to the power of negative 1 end exponent mu subscript 2 over mu subscript 1 equals sin to the power of negative 1 end exponent fraction numerator 1.0 over denominator 1.25 end fraction equals sin to the power of negative 1 end exponent 100 over 125 equals sin to the power of negative 1 end exponent 4 over 5 theta to the power of " equals sin to the power of negative 1 end exponent 4 over 5 sin space theta to the power of " equals 4 over 5 c o n i d e r space t r i a n g l e space m a k i n g space b y space r a y sin c e comma space space space theta to the power of " equals straight pi over 2 minus theta to the power of apostrophe t a k e space b o t h space s i d e space sin sin theta to the power of " equals sin left parenthesis straight pi over 2 minus theta to the power of apostrophe right parenthesis sin theta to the power of " equals cos theta to the power of apostrophe o r comma sin theta to the power of " equals cos theta to the power of apostrophe equals 4 over 5 u s e space p y t h a g o r o u s space t h e o r e m space a n d space f i n d space sin theta to the power of apostrophe s o comma space sin theta to the power of apostrophe equals 3 over 5 f r o m space s n e l l apostrophe s space l a w fraction numerator sin theta over denominator sin theta to the power of apostrophe end fraction equals fraction numerator 1.25 over denominator 1 end fraction equals 1.25 sin theta equals 1.25 cross times sin theta to the power of apostrophe sin theta equals 1.25 cross times 3 over 5 equals 3 over 4 sin theta equals 3 over 4 theta equals sin to the power of negative 1 end exponent 3 over 4 i f space theta to the power of " space i s space t h e space g r e a t e r space t h a n space t h e space c r i t i c a l space a n g l e comma space theta space w i l l space b e space s m a l l e r space t h a n space t h i s space v a l u e t h u s comma space theta subscript m a x end subscript comma w h i c h space t o t a l space r e f l e c t i o n space t a k e s space p l a c e space a t space t h e space v e r t i c l e space s u r f a c e comma i s space space theta subscript m a x end subscript equals sin to the power of negative 1 end exponent left parenthesis 3 over 4 right parenthesis
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