question_answer

An eye specialist prescribes spectacles having combination of convex lens of focal length 40 cm in contact with a concave lens of focal length 25 cm. The power of this lens combination in diopters is

A) +1.5

B) -1.5

C) +6.67

D) -6.67

Correct Answer: B

Solution :

[b] \[{{f}_{1}}=+40cm=0.4m\] (for convex lens)    \[{{f}_{2}}=-25cm=-0.25m\] (for concave lens)    \[\therefore \]Focal length (f) of the combination \[\frac{1}{f}=\frac{1}{{{f}_{1}}}+\frac{1}{{{f}_{2}}}=\frac{1}{0.40}-\frac{1}{0.25}=\frac{0.25-0.4}{0.40\times 0.25}\] \[=-\frac{0.15}{0.1}=-1.5\text{ dioptre}\text{.}\Rightarrow \text{P=}\frac{1}{f}=-1.5\text{ dioptre}\]