an equiconvex lens is placed over a plane mirror as indicated in diagram and object placed 12 cm from system such that image and object inside a liquid is power between mirror and lens and for the same object Rai image now formed at 24 cm from the refractive index of the liquid word will be system such that image and object inside now you liquid is power between mirror and

Asked by pavansguntur | 12th May, 2020, 04:00: PM

Expert Answer:

F o c a l space l e n g t h space o f space e q u i c o n v e x space l e n s space f 1 space equals space 12 space c m space

T h e space l i q u i d space p o u r e d space i s space l i k e space a space m i r r o r. space L e t space t h e space f o c a l space l e n g t h space o f space l i q u i d space b e space f subscript 2 space

F o c a l space l e n g t h space o f space s y s t e m space left parenthesis c o n v e x space l e n s space plus space l i q u i d right parenthesis space equals space 24 space c m space

E q u i v a l e n t space f o c a l space l e n g t h space
1 over f equals space 1 over f subscript 1 space plus space 1 over f subscript 2 space
1 over 24 space equals space 1 over 12 space plus 1 over f subscript 2 space

1 over f subscript 2 space equals space 1 over 24 minus 1 over 12 space space

T h u s comma space
f 2 space equals space minus 24 space c m space

R e f r a c t i v e space i n d e x space o f space l e n s space mu subscript 1 space equals space 3 divided by 2 space

R a d i u s space o f space c u r v a t u r e space a r e space R space a n d space minus space R space
1 over f subscript 1 space equals left parenthesis mu subscript 1 space space minus space 1 right parenthesis space open parentheses 1 over R minus space fraction numerator 1 over denominator negative R end fraction close parentheses space
1 over 12 space equals space open parentheses 3 over 2 space space minus space 1 close parentheses space 2 over R space

R space equals space 24 open parentheses 1 half close parentheses space equals space 12 space c m space

L e t space R I space o f space l i q u i d space b e space mu subscript 2 space
T h e space r a d i u s space o f space c u r v a t u r e space o f space l i q u i d space i n space p l a n e space m i r r o r space s i d e space w i l l space b e space infinity space

R a d i u s space o f space c u r v a t u r e space o f space l i q u i d space i n space l e n s space s i d e space R space equals space minus 12 space c m space
1 over f subscript 2 space equals space open parentheses mu subscript 2 minus space 1 close parentheses open parentheses 1 over R minus space 1 over infinity close parentheses
fraction numerator 1 over denominator negative 24 end fraction space equals space space open parentheses mu subscript 2 minus space 1 close parentheses open parentheses fraction numerator 1 over denominator negative 12 end fraction minus space 1 over infinity close parentheses space

fraction numerator 1 over denominator negative 24 end fraction space equals space space open parentheses mu subscript 2 minus space 1 close parentheses open parentheses fraction numerator 1 over denominator negative 12 end fraction close parentheses space
fraction numerator negative 12 over denominator negative 24 end fraction space equals space space open parentheses mu subscript 2 minus space 1 close parentheses space
1 half space plus 1 space equals space mu subscript 2 space space

space mu subscript 2 space equals space 3 over 2

space

Answered by Shiwani Sawant | 12th May, 2020, 09:31: PM