A) \[{{x}_{1}}{{x}_{2}}\]
B) \[\sqrt{{{x}_{1}}{{x}_{2}}}\]
C) \[\frac{{{x}_{1}}+{{x}_{2}}}{2}\]
D) \[\sqrt{\frac{{{x}_{1}}}{{{x}_{2}}}}\]
Correct Answer: B
Solution :
Given \[u=(f+{{x}_{1}})\] and \[v=(f+{{x}_{2}})\] The focal length \[f=\frac{uv}{u+v}=\frac{(f+{{x}_{1}})(f+{{x}_{2}})}{(f+{{x}_{1}})+(f+{{x}_{2}})}\] On solving, we get \[{{f}^{2}}={{x}_{1}}{{x}_{2}}\] or \[f=\sqrt{{{x}_{1}}{{x}_{2}}}\]
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