A) \[\frac{{{f}_{1}}+{{f}_{2}}}{2}\]
B) \[\sqrt{{{f}_{1}}}{{f}_{2}}\]
C) \[\frac{{{f}_{1}}{{f}_{2}}}{{{f}_{1}}+{{f}_{2}}}\]
D) \[\frac{{{f}_{1}}{{f}_{2}}}{{{f}_{1}}-{{f}_{2}}}\]
Correct Answer: C
Solution :
When\[{{f}_{1}}\]and\[{{f}_{2}}\]are focal lengths of lenses combined together, image formation takes place as follows, From lens formula \[\frac{1}{v}-\frac{1}{u}=\frac{1}{{{f}_{1}}}\] ?. (i) \[\frac{1}{v}-\frac{1}{v}=\frac{1}{{{f}_{2}}}\] ?.(ii) Adding Eqs. (i) and (ii), we get \[\frac{1}{v}-\frac{1}{u}=\frac{1}{{{f}_{1}}}+\frac{1}{{{f}_{2}}}\] If this lens is replaced by a single lens, then focal length of combination is \[\frac{1}{F}=\frac{1}{{{f}_{1}}}+\frac{1}{{{f}_{2}}}=\frac{1}{v}-\frac{1}{u}\] \[\Rightarrow \] \[F=\frac{{{f}_{1}}{{f}_{2}}}{{{f}_{1}}+{{f}_{2}}}\]You need to login to perform this action.
You will be redirected in
3 sec