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Wave Optics

Question
CBSEENPH12039501

A thin convex lens made from crown glass open parentheses straight mu space equals space 3 over 2 close parentheses has focal length f. When it is measured in two different liquids having refractive indices 4/3 and 5/3, it has the focal lengths f1 and f2 respectively. The correct

  •  f1  = f2 <f

  •  f1  >f and f2 becomes negative

  •  f2  >f and f1 becomes negative

  • f1 and f2 both become negative

Solution

B.

 f1  >f and f2 becomes negative

according to lens maker's formula, when the lens in the air.
1 over straight f space equals space open parentheses 3 over 2 minus 1 close parentheses open parentheses 1 over straight R subscript 1 minus 1 over straight R subscript 2 close parentheses
1 over straight f space equals space fraction numerator 1 over denominator 2 straight x end fraction rightwards double arrow space straight f space equals 2 straight x
Here comma space open parentheses 1 over straight x space equals space 1 over straight R subscript 1 minus 1 over straight R subscript 2 close parentheses
In case of liquid, where refractive index is 4/3 and 5/3
we get
Focal length in first liquid
1 over straight f subscript 1 space equals space open parentheses straight mu subscript straight s over straight mu subscript straight l subscript 2 end subscript minus 1 close parentheses open parentheses 1 over straight R subscript 1 minus 1 over straight R subscript 2 close parentheses
1 over straight f subscript 1 space equals space open parentheses fraction numerator begin display style 3 over 2 end style over denominator begin display style 4 over 3 end style end fraction minus 1 close parentheses space 1 over straight x
⇒ f1 is positive.
1 over straight f subscript 1 space minus space fraction numerator 1 over denominator 8 straight x end fraction space equals space fraction numerator 1 over denominator 4 left parenthesis 2 straight x right parenthesis end fraction space equals space fraction numerator 1 over denominator 4 straight f end fraction rightwards double arrow space straight f subscript 1 space equals space 4 straight f
Focal length in second liquid
1 over straight f subscript 2 space equals space open parentheses straight mu subscript straight s over straight mu subscript l subscript 2 end subscript minus 1 close parentheses open parentheses 1 over straight R subscript 1 minus 1 over straight R subscript 2 close parentheses
rightwards double arrow space 1 over straight f subscript 1 space equals space open parentheses fraction numerator begin display style 3 over 2 end style over denominator begin display style 5 over 3 end style end fraction minus 1 close parentheses open parentheses 1 over straight x close parentheses
rightwards double arrow space straight f subscript 2 space is space negative

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