A) 6.67
B) - 6.67
C) 33.3
D) - 33.3
Correct Answer: A
Solution :
[a]Focal length of plano-convex lens is 10 cm |
\[\frac{1}{10}=\left( \frac{3}{2}-1 \right)\left( \frac{1}{\infty }-\frac{1}{-R} \right)\] |
\[\frac{1}{10}=\frac{1}{2}\times \frac{1}{R}\Rightarrow R=5cm\] |
Let focal length of water lens is \[{{f}_{w}}\] |
\[\frac{1}{{{f}_{w}}}=\left( \frac{4}{3}-1 \right)\left( \frac{1}{-5}-\frac{1}{5} \right)\] |
\[\Rightarrow \] \[f=-\frac{15}{2}cm=-\frac{0.15m}{2}=-\frac{3}{40}m\] |
Optical powers of system |
\[P=\frac{1}{f}+\frac{1}{f}+\frac{1}{{{f}_{w}}}=\frac{1}{0.1}+\frac{1}{0.1}+\left( -\frac{40}{3} \right)=6.67D\] |
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