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Question
A combination of lenses for a camera contains two converging lenses of focal lengths 20 cm and 40 cm and a diverging lens of focal length 50 cm. Find the power and focal length of the combination.
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Solution
Focal length (f1) of the 1st converging lens = 20 cm = 0.2 m
Focal length (f2) of the 2nd converging lens = 40 cm = 0.4 m
Focal length (f3) of the diverging lens = −50 cm = −0.5 m (negative sign due to sign convention)
Power = `1/"Focal length of lens (in metre)"`
Power (P1) of 1st lens = `1/0.2` = 5 D
Power (P2) of 2nd lens = `1/0.4` = 2.5 D
Power (P3) of diverging lens = `1/0.5` = −2 D
Net power of the combination = P1 + P2 + P3
= 5 + 2.5 + (−2)
= 7.5 − 2
= 5.5 D
Net focal length of the combination = `1/"Net power"`
= `1/5.5`
= 0.1818 m
= 18.18 cm
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