Question

A lens of power $+2.0\text{D}$ is placed in contact with another lens of power $-1.0\text{D}$. The combination will behave like

• A. a converging lens of focal length $100\text{cm}$.
  
• B. a diverging lens of focal length $100\text{cm}$
• C. a converging lens of focal length $50\text{cm}$.
• D. a diverging lens of focal length $50\text{cm}$.

Answer 1

The correct option is A a converging lens of focal length $100\text{cm}$.


Using the formula, $P=\frac{1}{f\left(\text{in m}\right)}$
Given that
$P_1=2\text{D}$
$f_1=\frac{100}{2}=+50\text{cm}$
$f_2=100\text{cm}$
$\frac{1}{f_{eq}}=[\frac{1}{f_1}+\frac{1}{f_2}]$
$\frac{1}{f_{eq}}=[\frac{1}{50}-\frac{1}{100}]=\left[\frac{2-1}{100}\right]=\frac{1}{100}$
$f_{eq}=100\text{cm}$