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CBSE Class 12-science Answered

the focal lengths of objective and eye lense of a microscope are 1.6 and 2.5 cm .the distance between the two lenses is 21.7cm.if the final image is formed at infinity the distance between the object and the objective lens is ?(ans.1.75cm)
Asked by Nidhi | 26 Dec, 2014, 01:42: PM
answered-by-expert Expert Answer
Let vo be the distance between the image and objective lens and
uo be the distance between the object and the objective lens.
Given that the final image is formed at infinity.
In such a case we know that the length of the microscope is given by:
 
begin mathsize 14px style straight L space equals straight v subscript straight o plus straight f subscript straight e Where space straight L space is space the space length space of space the space microscope space and space straight f subscript straight e space space the space focal space length space of space t h e space objective. Given space straight L space equals 21.7 cm space comma space straight f subscript straight e space equals 2.5 space cm Substituting space we space get : 21.7 space equals straight v subscript straight o space plus 2.5 space rightwards double arrow straight v subscript straight o space equals 21.7 minus 2.5 space equals 19.2 space cm According space to space lens space formula space we space know space that : 1 over straight f subscript straight o equals 1 over straight v subscript straight o minus 1 over straight u subscript straight o straight f subscript straight o space equals 1.6 space cm space comma space straight v subscript straight o equals space 19.2 space cm space comma space straight u subscript straight o space equals ? fraction numerator 1 over denominator 1.6 end fraction equals fraction numerator 1 over denominator 19.2 end fraction minus 1 over straight u subscript straight o minus 1 over straight u subscript straight o equals fraction numerator 1 over denominator 1.6 end fraction minus fraction numerator 1 over denominator 19.2 end fraction minus 1 over straight u subscript straight o equals 10 over 16 minus 10 over 192 minus 1 over straight u subscript straight o equals fraction numerator 120 minus 10 over denominator 192 end fraction equals 110 over 192 straight u subscript straight o space equals minus 192 over 110 cm space equals minus 1.75 space c m end style
Therefore the distance between the object and the objective lens is 1.75 cm
Answered by Jyothi Nair | 27 Dec, 2014, 09:50: PM

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