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a) Determine the 'eefective focal length' of the combination of the two lenses in Exercise 10, if they are placed 8.0 cm apart with their principal axes coincident. Does the answer depend on which side of the combination a beam of parallel light is incident ? Is the notion of effective focal length of this system useful at all ? |
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Answer» Solution :i) Let a parallel beam be incident on the convex LENS first. If 2nd lens were absent, then `u_(1)=oo and f_(1)=30cm` As `(1)/(upsilon_(1))-(1)/(u_(1))=(1)/(f_(1))` `(1)/(upsilon_(1))=(1)/(oo)=(1)/(30)` `upsilon_(1)=30cm` The image would now act as a virtual object for 2nd lens. `u_(2)=+(30-8)=+22cm` `upsilon_(2)=?, f_(2)=-20cm` As `(1)/(upsilon_(2))=(1)/(f_(2))+(1)/(u_(2))` `(1)/(upsilon_(2))=(1)/(-20)+(1)/(22)=(-11+10)/(220)=(-1)/(220)` `upsilon_(2)=-220cm` `therefore` Parallel incident beam would appear to diverge from a point `220-4=216cm` from the centre of the two lens system. ii) Suppose a parallel beam of light fromthe LEFT is incident first on the concave lens. `u_(1)=-oo, f_(1)=-20cm, upsilon=?` As `(1)/(upsilon_(1))-(1)/(u_(1))=(1)/(f_(1))` `(1)/(upsilon_(1))=(1)/(f_(1))+(1)/(u_(1))=(-1)/(20)+(1)/(-oo)=(-1)/(20)` This image acts as a real object for the 2nd lens. `u_(2)=-(20+8)=-28cm, f_(2)=30cm,` `upsilon_(2)=?` As `(1)/(upsilon_(2))-(1)/(u_(2))=(1)/(f_(2))` `(1)/(upsilon_(2))=(1)/(f_(2))+(1)/(u_(2))=(1)/(30)-(1)/(28)=(14-15)/(420)` `upsilon_(2)=-420 CM` `therefore` The parallel beam appears to diverge from a point `420-4=416cm`, on the left of the centre of the two lens system. From the above discussion, we observe that the anwer depends on which side of the lens system the parallel beam is incident. Therefore, the notion of effective focal length does not SEEM to be useful here. |
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