Just prove that they are parralel to each other

Asked by lovemaan5500 | 1st Dec, 2017, 11:32: AM

Expert Answer:

 
 

A t space t h e space p o i n t space o f space i n c i d e n c e space o n space s u r f a c e space A A space s n e l l apostrophe s space l a w space c a n space b e space g i v e n space a s

fraction numerator sin space i 1 over denominator sin space r 1 end fraction equals u subscript a over u subscript g

A t space t h e space p o i n t space o f space i n c i d e n c e space o n space s u r f a c e space B B space s n e l l apostrophe s space l a w space c a n space b e space g i v e n space a s

fraction numerator begin display style sin space i 2 end style over denominator begin display style sin space r 2 end style end fraction equals fraction numerator begin display style u subscript g end style over denominator begin display style u subscript a end style end fraction

i n space g l a s s space s l a b space A A space i s space p a r a l l e l space t o space B B space a n d space n o r m a l space a r e space p e r p e n d i c u l a r space h e n c e space t h e y space a l s o space a r e space p a r a l l e l

t h e r e f o r e space a n g l e space r 1 space equals space a n g l e space i 2 space a r e space e q u a l space b e c u a s e space t h e y space f o r m space a l t e r n a t e space a n g l e s

sin space r 1 equals space sin space i 2 space

f r o m space
fraction numerator begin display style sin space i 1 end style over denominator begin display style sin space r 1 end style end fraction equals fraction numerator begin display style u subscript a end style over denominator begin display style u subscript g end style end fraction

sin space i 1 space equals fraction numerator begin display style u subscript a end style over denominator begin display style u subscript g end style end fraction x space sin space r 1

f r o m space

fraction numerator begin display style sin space i 2 end style over denominator begin display style sin space r 2 end style end fraction equals fraction numerator begin display style u subscript g end style over denominator begin display style u subscript a end style end fraction space space

sin space r 2 equals space fraction numerator begin display style u subscript a end style over denominator begin display style u subscript g end style end fraction x space sin space i 2

t h e r e f o r e space space sin space i 1 equals sin space r 2

h e n c e space i n c i d e n t space r a y space a n d space e m e r g e n t space r a y space a r e space p a r a l l e l

Answered by Gajendra | 21st Dec, 2017, 01:37: PM

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