Q.56 The figure shows a convergent lens placed inside a cell filled with a liquid. The lens has a focal length +20 cm, when in air and its material has refractive index 1.5. if the liquid has a refractive index 1.6, the focal length of the system is
a) +80 cm
b) –80 cm
c) –24 cm
d) –160 cm

Asked by Malavika Umesh | 5th May, 2015, 06:16: PM

Expert Answer:

Given:
Focal length of lens= +20 cm
Refractive index in air = 1.5
Refractive index of liquid = 1.6
Focal length, F=?

 
By using,
begin mathsize 14px style 1 over straight f subscript 1 equals left parenthesis straight mu minus 1 right parenthesis open parentheses 1 over straight R subscript 1 minus 1 over straight R subscript 2 close parentheses  1 over straight f subscript 1 equals left parenthesis 1.6 minus 1 right parenthesis open parentheses 1 over infinity minus 1 over 20 close parentheses space space space space space space equals space 0.6 space open parentheses 0 minus comma 1 over 20 close parentheses space space space space space space equals space minus fraction numerator 0.6 over denominator 20 end fraction space space space space space space equals negative 3 over 100 space space space space space space... space left parenthesis 1 right parenthesis  1 over straight f subscript 2 equals left parenthesis 1.5 minus 1 right parenthesis open parentheses 1 over 20 minus fraction numerator 1 over denominator negative 20 end fraction close parentheses space space space space space space equals space 0.5 space open parentheses 1 over 20 plus comma 1 over 20 close parentheses space space space space space space equals space 0.5 open parentheses space fraction numerator 20 plus 20 over denominator 400 end fraction close parentheses space space space space space space equals 1 over 20 space space space space space space... space left parenthesis 2 right parenthesis  1 over straight f subscript 3 equals left parenthesis 1.6 minus 1 right parenthesis open parentheses fraction numerator 1 over denominator negative 20 end fraction minus 1 over infinity close parentheses space space space space space space equals space 0.6 space open parentheses fraction numerator 1 over denominator negative 20 end fraction minus 0 close parentheses space space space space space space equals space minus fraction numerator 0.6 over denominator 20 end fraction space space space space space space equals negative 3 over 100 space space space space space space... space left parenthesis 3 right parenthesis  space end style
 
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Answered by Faiza Lambe | 5th May, 2015, 08:31: PM