Question. (a) Give quantitative as well as qualitative explanation behind the facti thatachromatism of both position and magnification is not possible by using two thin lenses separated by a distance.
(b)Derive and discuss the condition of achromatism for two thin lenses of focali lengths f, and f, when they are made of different materials but placed in contact.
(c) Suppose you have an object and you are using both the Huygen's eye-piece andi Ramsdon's eye-piece to get an enlarged image of the object. What are thei differences and shortcomings will you observed in the images formed by the two cye-pieces. Explain comparatively.
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Let two thin lenses are kept in contact.
For first lens we have
fv1=(nv−1)(R11−R21)
and fR1=(nR−1)(R11−R21)
fV1−fR1=(nV−nR)(R11−R21)
=(nY−1)(nV−nR)(nY−1)(R11−R21)=fYω
or fV′1−fR1=fω (Letfy=f) ..... (1)
Similarly for second lens
fV′1−fR′1=f′ω′ ......... (2)
Adding equations (1) and (2)
(fV1+fV′1)−(fR1+fR′1)=fω+f′ω′ ....... (3)
If the focal length of this lens combination for violet and red rays be FV and FR respectively then
fV1+fV′1=FV1
and fR1+fR′1=FR1
So equation (3) becomes
FV1−FR1=fω+f′ω′
But for achromatism of the lens combination, the focal length must be same for all colours of light so, FV=FR
So, fω+f′ω′=0
i.e., fω+f′ω′=0
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