A) 25 cm
B) 20 cm
C) 30 cm
D) 40 cm
Correct Answer: A
Solution :
Key Idea: For an achrometic combination powers are additive in nature. When two lenses of different powers are combined, the power of combination is sum of individual powers \[\therefore \] \[P={{P}_{1}}+{{P}_{2}}\] \[\therefore \] \[P=3D+(-5D)=-2D\] Also power \[=\frac{1}{{{f}_{(metres)}}}\]diopters \[\therefore \] \[f=\frac{100}{P}=-\frac{100}{2}\,m\] \[=-50\,m\] From lens formula \[\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\] Putting\[f=-50\,cm,\,u=-50\,cm\] \[-\frac{1}{50}=\frac{1}{v}-\left( -\frac{1}{50} \right)\] \[\Rightarrow \] \[v=-25\,cm\] Hence, image is formed at same side as object. Note: Since, focal length is negative, it is a diverging lens.
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