A) \[\sqrt{\frac{{{f}_{1}}}{{{f}_{2}}}}\]
B) \[\sqrt{\frac{{{f}_{2}}}{{{f}_{1}}}}\]
C) \[\frac{{{f}_{1}}+{{f}_{2}}}{{{f}_{1}}{{f}_{2}}}\]
D) \[\frac{{{f}_{1}}+{{f}_{2}}}{{{f}_{1}}{{f}_{2}}}\]
Correct Answer: D
Solution :
If two thin lenses of focal lengths \[{{f}_{1}},{{f}_{2}}\]are placed in contact coaxially, then equivalent focal length of combination is \[\frac{1}{F}=\frac{1}{{{f}_{1}}}+\frac{1}{{{f}_{2}}}-\frac{0}{{{f}_{1}}{{f}_{2}}}=\frac{1}{{{f}_{1}}}+\frac{1}{{{f}_{2}}}\] Power for the combination is \[P=\frac{1}{F}=\frac{1}{{{f}_{1}}}+\frac{1}{{{f}_{2}}}=\frac{{{f}_{1}}+{{f}_{2}}}{{{f}_{1}}{{f}_{2}}}\]
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