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Geometrical Optics question

2016 · Q130
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Geometrical Optics question

2016 · Q130

NEETPhysicsGeometrical OpticsMCQ+4 / −1
Two identical glass (μ\muμg = 3/2) equiconvex lenses of focal length fff each are kept in contact. The space between the two lenses is filled with water (μw=4/3)\left( {{\mu _w} = 4/3} \right)(μw​=4/3). The focal length of the combination is
  1. A
    f/3f/3f/3
  2. B
    fff
  3. C
    4f/34f/34f/3
  4. D
    3f/43f/43f/4
View written solutionFree

Correct answer: D

NEET 2016 Phase 2 Physics - Geometrical Optics Question 76 English Explanation


Focal length (f) of glass convex lens is given by

$${1 \over f} = \left( {{\mu _g} - 1} \right)\left( {{2 \over R}} \right)$$

$ \Rightarrow $ $${1 \over f} = \left( {{3 \over 2} - 1} \right)\left( {{2 \over R}} \right)$$

$ \Rightarrow $ f = R

Focal length (f1) of water filled concave lens is given by

$${1 \over {{f_1}}} = \left( {{\mu _w} - 1} \right)\left( { - {2 \over R}} \right)$$

$ \Rightarrow $ $${1 \over {{f_1}}} = \left( {{4 \over 3} - 1} \right)\left( { - {2 \over R}} \right)$$ = ${ - {2 \over {3R}}}$ = ${ - {2 \over {3f}}}$

Equivalent focal length (feq) of lens system

$${1 \over {{f_{eq}}}} = {1 \over f} - {2 \over {3f}} + {1 \over f}$$ = ${4 \over {3f}}$

$ \therefore $ feq = ${{3f} \over 4}$
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