A) \[\frac{R}{2({{\mu }_{1}}+{{\mu }_{2}})}\]
B) \[\frac{R}{2({{\mu }_{1}}-{{\mu }_{2}})}\]
C) \[\frac{R}{({{\mu }_{1}}-{{\mu }_{2}})}\]
D) \[\frac{2R}{({{\mu }_{2}}-{{\mu }_{1}})}\]
Correct Answer: C
Solution :
Focal length of the combination \[\frac{1}{f}=\frac{1}{{{f}_{1}}}+\frac{1}{{{f}_{2}}}\] ?(i) We have \[{{f}_{1}}=\frac{R}{({{\mu }_{1}}-1)}\]and \[{{f}_{2}}=\frac{R}{({{\mu }_{2}}-1)}\] or \[\frac{1}{{{f}_{1}}}=\frac{R}{({{\mu }_{1}}-1)}\]or \[\frac{1}{{{f}_{2}}}=-\frac{R}{({{\mu }_{2}}-1)}\] Putting these values in Eq. (i), we get \[\frac{1}{f}=\frac{({{\mu }_{1}}-1)}{R}-\frac{({{\mu }_{2}}-1)}{R}.\] \[=\frac{[{{\mu }_{1}}-1-{{\mu }_{2}}+1]}{R}=\frac{{{\mu }_{1}}-{{\mu }_{2}}}{R}\]You need to login to perform this action.
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