Q.Two thin lenses of focal lengths $+12\ \text{cm}$ and $-20\ \text{cm}$ are placed in contact. Calculate the focal length and power of the combination and state whether the combined system converges or diverges a parallel beam.

$\dfrac1F=\dfrac1{f_1}+\dfrac1{f_2}=\dfrac1{12}+\dfrac1{-20}=\dfrac1{12}-\dfrac1{20}=\dfrac{5-3}{60}=\dfrac2{60}=\dfrac1{30}$, so $F=30\ \text{cm}=0.30\ \text{m}$, giving power $P=1/F=1/0.30\approx3.33\ \text{D}$ (or directly, $P_1+P_2=100/12-100/20\approx8.33-5=3.33\ \text{D}$). Since $F$ and $P$ both come out positive, the combination as a whole is converging, even t …

Add the reciprocals of the two (correctly signed) focal lengths to find $ …

• Forgetting the negative sign on the $-20\ \text{cm}$ diverging lens's focal length before adding. …