A combination of lenses for a camera contains two converging lenses of focal lengths 20cm and 40cm and a diverging lens of focal length 50cm. Find the power and focal length of the combination.
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$\text{f}_1=20\text{cm}=0.2\text{m}$$\text{P}_1=\frac{1}{\text{f}_1}=\frac{1}{0.2}=+5\text{D}$
$\text{f}_2=40\text{cm}=0.4\text{m}$
$\text{P}_2=\frac{1}{\text{f}_2}=\frac{1}{0.4}=+2.5\text{D}$
$\text{f}_3=-50\text{cm}=-0.5\text{m}$
$\text{P}_3=\frac{1}{\text{f}_3}=\frac{1}{-0.5}=-2\text{D}$
Power of the combination,
$\text{P}=\text{P}_1+\text{P}_2+\text{P}_3$
$=+5\text{D}+2.5\text{D}+(-2\text{D})$
$=+5.5\text{D}$
Focal length of the combination,
$\text{f}=\frac{1}{\text{P}}=\frac{1}{+5.5}=+0.1818\text{m}=+18.18\text{cm}$
$\text{f}_2=40\text{cm}=0.4\text{m}$
$\text{P}_2=\frac{1}{\text{f}_2}=\frac{1}{0.4}=+2.5\text{D}$
$\text{f}_3=-50\text{cm}=-0.5\text{m}$
$\text{P}_3=\frac{1}{\text{f}_3}=\frac{1}{-0.5}=-2\text{D}$
Power of the combination,
$\text{P}=\text{P}_1+\text{P}_2+\text{P}_3$
$=+5\text{D}+2.5\text{D}+(-2\text{D})$
$=+5.5\text{D}$
Focal length of the combination,
$\text{f}=\frac{1}{\text{P}}=\frac{1}{+5.5}=+0.1818\text{m}=+18.18\text{cm}$
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