How we can prove that :

Refractive index = real depth/ apparent depth

Asked by Ritachoudhary697 | 13th Jun, 2019, 05:29: PM

Expert Answer:

tani=Sini=AB/object distance
tanr=Sinr=AB/Image distance
fraction numerator S i n i over denominator S i n r end fraction equals fraction numerator I m a g e space d i s tan c e space over denominator O b j e c t space d i s tan c e end fraction
A s space t h e space r a y space o f space l i g h t space i s space g o i n g space f r o m space d e n s e r left parenthesis mu subscript 1 right parenthesis space m m e d i u m space t o space r a r e r left parenthesis mu subscript 2 right parenthesis space m e d i u m space
fraction numerator begin display style mu subscript 2 end style over denominator begin display style mu subscript 1 end style end fraction equals fraction numerator begin display style I m a g e space d i s tan c e space end style over denominator begin display style O b j e c t space d i s tan c e end style end fraction
fraction numerator begin display style mu subscript 2 end style over denominator begin display style mu subscript 1 end style end fraction equals fraction numerator begin display style A p p a r e n t space d e p t h space end style over denominator begin display style R e a l space d e p t h end style end fraction
I f space t h e space r a r e r space m e d i u m space i s space a i r space h a v i n g space r e f r a c t i v e space i n d e x space mu subscript 2 equals 1
1 over mu equals fraction numerator begin display style A p p a r e n t space d e p t h space end style over denominator begin display style R e a l space d e p t h end style end fraction
fraction numerator begin display style R e a l space d e p t h space end style over denominator begin display style A p p a r e n t space d e p t h end style end fraction equals mu
mu subscript 1 equals mu

Answered by Utkarsh Lokhande | 13th Jun, 2019, 07:05: PM