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Question
Two lenses in contact made of materials with dispersive powers in the ratio 2 : 1, behave as an achromatic lens of focal length 10 cm. The individual focal lengths of the lenses are
Two lenses in contact made of materials with dispersive powers in the ratio 2 : 1, behave as an achromatic lens of focal length 10 cm. The individual focal lengths of the lenses are
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Solution
The correct option is D 5 cm, -10 cm
Dispersive power of a lens ∝1μ−1
Thus ω1ω2=μ2−1μ1−1=2
Thus μ2=2μ1−1
From lens maker's formula we knowf∝1μ−1
This gives f1f2=−μ2−1μ1−1=−2(- sign comes from the opposite sign of R in convex and concave lenses).
1f=1f2+1f2
This gives f1=5,f2=−10
Dispersive power of a lens ∝1μ−1
Thus ω1ω2=μ2−1μ1−1=2
Thus μ2=2μ1−1
From lens maker's formula we know
f∝1μ−1
This gives f1f2=−μ2−1μ1−1=−2(- sign comes from the opposite sign of R in convex and concave lenses).
1f=1f2+1f2
This gives f1=5,f2=−10
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